D Khoshnevisan
  • Professor, Mathematics

Publications

  • Davar Khoshnevisan & Robert C. Dalang and Tusheng Zhang (2019). Global solutions to reaction-diffusion equations with super-linear drift and multiplicative noise. The Annals of Probability. Vol. 47(1), 519-559. Published, 01/2019.
  • Davar Khoshnevisan, Nicos Georgiou, Kunwoo Kim & Alex D. Ramos (2018). The dimension of the range of a random walk. Electronic Journal of Probability. 1-31. Published, 01/2018.
  • Davar Khoshnevisan & Kunwoo Kim, Yimin Xiao (2018). A macroscopic multifractal analysis of parabolic stochastic PDEs. Communications in Mathematical Physics. Vol. 360, 307-346. Published, 01/2018.
  • Khoshnevisan, Davar (2016). From Levy-type Processes to Parabolic SPDEs. Birkhauser. Published, 10/20/2016.
  • Khoshnevisan, Davar & Xiao, Yimin (2015). Brownian motion and thermal capacity. Institute of Mathematical Statistics. Vol. 43(1), 405-434. Published, 2015.
  • Khoshnevisan, Davar, Mahboubi, Pejman & Foondun, Mohammud (2015). Analysis of the gradient of the solution to a stochastic heat equation via fractional Brownian motion. Springer Nature. Vol. 3(2), 133-158. Published, 2015.
  • Khoshnevisan, Davar & Kim, Kunwoo (2015). Non-linear noise excitation and intermittency under high disorder. American Mathematical Society (AMS). 1. Published, 2015.
  • Georgiou, Nicos, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2015). Semi-discrete semi-linear parabolic SPDEs. Institute of Mathematical Statistics. Vol. 25(5), 2959-3006. Published, 2015.
  • Khoshnevisan, Davar & Xiao, Yimin (2015). Brownian motion and thermal capacity. Institute of Mathematical Statistics. Vol. 43(1), 405-434. Published, 2015.
  • Khoshnevisan, Davar, Mahboubi, Pejman & Foondun, Mohammud (2015). Analysis of the gradient of the solution to a stochastic heat equation via fractional Brownian motion. Springer Nature. Vol. 3(2), 133-158. Published, 2015.
  • Khoshnevisan, Davar & Kim, Kunwoo (2015). Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups. Institute of Mathematical Statistics. Vol. 43(4), 1944-1991. Published, 2015.
  • Georgiou, Nicos, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2015). Semi-discrete semi-linear parabolic SPDEs. Institute of Mathematical Statistics. Vol. 25(5), 2959-3006. Published, 2015.
  • Conus, Daniel, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2014). Initial measures for the stochastic heat equation. Institute of Mathematical Statistics. Vol. 50(1), 136-153. Published, 2014.
  • The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a “random noise,” also known as a “generalized random field.” At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. Published, 05/2014.
    http://bookstore.ams.org/cbms-119
  • Foondun, Mohammud & Khoshnevisan, Davar (2013). Corrections and improvements to: “On the stochastic heat equation with spatially-colored random forcing”. American Mathematical Society (AMS). Vol. 366(1), 561-562. Published, 2013.
  • Conus, Daniel, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2013). Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1. Springer Science + Business Media. Vol. 34, 251-279. Published, 2013.
  • Conus, Daniel, Joseph, Mathew & Khoshnevisan, Davar (2013). On the chaotic character of the stochastic heat equation, before the onset of intermitttency. Institute of Mathematical Statistics. Vol. 41(3B), 2225-2260. Published, 2013.
  • Conus, Daniel, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2013). On the chaotic character of the stochastic heat equation, II. Springer Science + Business Media. Vol. 156(3-4), 483-533. Published, 2013.
  • Foondun, Mohammud & Khoshnevisan, Davar (2013). Corrections and improvements to: “On the stochastic heat equation with spatially-colored random forcing”. American Mathematical Society (AMS). Vol. 366(1), 561-562. Published, 2013.
  • Conus, Daniel, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2013). Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1. Springer Science + Business Media. Vol. 34, 251-279. Published, 2013.
  • Conus, Daniel, Joseph, Mathew & Khoshnevisan, Davar (2013). On the chaotic character of the stochastic heat equation, before the onset of intermitttency. Institute of Mathematical Statistics. Vol. 41(3B), 2225-2260. Published, 2013.
  • Conus, Daniel, Joseph, Mathew, Khoshnevisan, Davar & Shiu, Shang-Yuan (2013). On the chaotic character of the stochastic heat equation, II. Springer Science + Business Media. Vol. 156(3-4), 483-533. Published, 2013.
  • Xiao, Yimin, Wu, Dongsheng, Nualart, Eulalia, Dalang, Robert C. & Khoshnevisan, Davar (2012). Critical Brownian sheet does not have double points. Institute of Mathematical Statistics. Vol. 40(4), 1829-1859. Published, 2012.
  • Joseph, Mathew, Khoshnevisan, Davar & Conus, Daniel (2012). Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs. Institute of Mathematical Statistics. Vol. 17(0). Published, 2012.
  • Foondun, Mohammud & Khoshnevisan, Davar (2012). An asymptotic theory for randomly forced discrete nonlinear heat equations. Bernoulli Society for Mathematical Statistics and Probability. Vol. 18(3), 1042-1060. Published, 2012.
  • Xiao, Yimin, Wu, Dongsheng, Nualart, Eulalia, Dalang, Robert C. & Khoshnevisan, Davar (2012). Critical Brownian sheet does not have double points. Institute of Mathematical Statistics. Vol. 40(4), 1829-1859. Published, 2012.
  • Khoshnevisan, Davar & Foondun, Mohammud (2012). On the stochastic heat equation with spatially-colored random forcing. American Mathematical Society (AMS). Vol. 365(1), 409-458. Published, 2012.
  • Khoshnevisan, D., Schilling, R. L. & Xiao, Y. (2012). Packing dimension profiles and Levy processes. Oxford University Press (OUP). Vol. 44(5), 931-943. Published, 2012.
  • Conus, Daniel & Khoshnevisan, Davar (2012). On the existence and position of the farthest peaks of a family of stochastic heat and wave equations. Springer Science + Business Media. Vol. 152(3-4), 681-701. Published, 2012.
  • Joseph, Mathew, Khoshnevisan, Davar & Conus, Daniel (2012). Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs. Institute of Mathematical Statistics. Vol. 17(0). Published, 2012.
  • Foondun, Mohammud & Khoshnevisan, Davar (2012). An asymptotic theory for randomly forced discrete nonlinear heat equations. Bernoulli Society for Mathematical Statistics and Probability. Vol. 18(3), 1042-1060. Published, 2012.
  • Khoshnevisan, Davar & Foondun, Mohammud (2012). On the stochastic heat equation with spatially-colored random forcing. American Mathematical Society (AMS). Vol. 365(1), 409-458. Published, 2012.
  • Khoshnevisan, D., Schilling, R. L. & Xiao, Y. (2012). Packing dimension profiles and Levy processes. Oxford University Press (OUP). Vol. 44(5), 931-943. Published, 2012.
  • Khoshnevisan, Davar, Nualart, Eulalia & Foondun, Mohammud (2011). A local-time correspondence for stochastic partial differential equations. American Mathematical Society (AMS). Vol. 363(05), 2481-2481. Published, 2011.
  • Eisenbaum, Nathalie, Foondun, Mohammud & Khoshnevisan, Davar (2011). Dynkin’s Isomorphism Theorem and the Stochastic Heat Equation. Springer Science + Business Media. Vol. 34(3), 243-260. Published, 2011.
  • Hu, Yueyun, Khoshnevisan, Davar & Wouts, Marc (2011). Charged Polymers in the Attractive Regime: A First-Order Transition from Brownian Scaling to Four-Point Localization. Springer Science + Business Media. Vol. 144(5), 948-977. Published, 2011.
  • Eisenbaum, Nathalie, Foondun, Mohammud & Khoshnevisan, Davar (2011). Dynkin’s Isomorphism Theorem and the Stochastic Heat Equation. Springer Science + Business Media. Vol. 34(3), 243-260. Published, 2011.
  • Hu, Yueyun, Khoshnevisan, Davar & Wouts, Marc (2011). Charged Polymers in the Attractive Regime: A First-Order Transition from Brownian Scaling to Four-Point Localization. Springer Science + Business Media. Vol. 144(5), 948-977. Published, 2011.
  • Khoshnevisan, Davar, Nualart, Eulalia & Foondun, Mohammud (2011). A local-time correspondence for stochastic partial differential equations. American Mathematical Society (AMS). Vol. 363(05), 2481-2481. Published, 2011.
  • Khoshnevisan, Davar (2011). Multiparameter Processes. Springer Verlag. Published, 07/01/2011.
  • Khoshnevisan, Davar (2011). Multiparameter Processes. Springer Verlag. Published, 07/01/2011.
  • Khoshnevisan, Davar (2011). Multiparameter Processes. Springer Verlag. Published, 07/01/2011.
  • A local-time correspondence for stochastic partial differential equations, Transactions of the Amer. Math. Soc. Vol. 363(5):2481-2515 (with M. Foondun and E. Nualart). Published, 01/2011.
    http://www.math.utah.edu/~davar/PPT/FKNLocalTimeSP...
  • Hu, Yueyun & Khoshnevisan, Davar (2010). Strong approximations in a charged-polymer model. Springer Science + Business Media. Vol. 61(1-2), 213-224. Published, 2010.
  • Khoshnevisan, Davar & Foondun, Mohammud (2010). On the global maximum of the solution to a stochastic heat equation with compact-support initial data. Institute of Mathematical Statistics. Vol. 46(4), 895-907. Published, 2010.
  • Hu, Yueyun & Khoshnevisan, Davar (2010). Strong approximations in a charged-polymer model. Springer Science + Business Media. Vol. 61(1-2), 213-224. Published, 2010.
  • Khoshnevisan, Davar, Shieh, Narn-Rueih & Xiao, Yimin (2009). Hausdorff dimension of the contours of symmetric additive Lévy processes. Springer Science + Business Media. Vol. 143(3-4), 665-666. Published, 2009.
  • Khoshnevisan, Davar & Xiao, Yimin (2009). Harmonic analysis of additive Lévy processes. Springer Science + Business Media. Vol. 145(3-4), 459-515. Published, 2009.
  • Khoshnevisan, Davar & Foondun, Mohammud (2009). Intermittence and nonlinear parabolic stochastic partial differential equations. Institute of Mathematical Statistics. Vol. 14(0). Published, 2009.
  • Khoshnevisan, Davar & Xiao, Yimin (2009). Harmonic analysis of additive Lévy processes. Springer Science + Business Media. Vol. 145(3-4), 459-515. Published, 2009.
  • Khoshnevisan, Davar, Shieh, Narn-Rueih & Xiao, Yimin (2009). Hausdorff dimension of the contours of symmetric additive Lévy processes. Springer Science + Business Media. Vol. 143(3-4), 665-666. Published, 2009.
  • Dalang, Robert C., Khoshnevisan, Davar & Nualart, Eulalia (2009). Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise. Springer Science + Business Media. Vol. 144(3-4), 371-427. Published, 2009.
  • Khoshnevisan, Davar & Foondun, Mohammud (2009). Intermittence and nonlinear parabolic stochastic partial differential equations. Institute of Mathematical Statistics. Vol. 14(0). Published, 2009.
  • Hitting probabilities for systems of nonlinear stochastic heat equations with multiplicative noise (with Robert C. Dalang and Eulalia Nualart) Probability Theory and Related Fields 177, 371-427. Published, 2009.
  • From fractals and probability to Levy processes and stochastic PDEs Progress in Probability, Vol. 61, 111-141. Published, 2009.
  • Intermittence and nonlinear stochastic partial differential equations (with Mohammud Foondun) Electronic J. Probab. Vol. 14, Paper no. 21, 548-568. Published, 2009.
  • Charged polymers and random walk in random scenery (with Xia Chen) In: Optimality: The Third Erich L. Lehmann Symposium, IMS Lecture Notes-Monograph Series, Vol. 57 (Javier Rojo, Editor), 237-251, IMS, Hayward, California. Published, 2009.
  • Harmonic analysis of additive Levy processes (with Yimin Xiao) Probability Theory and Related Fields 145, 459-515. Published, 2009.
  • Khoshnevisan, Davar (2008). A Minicourse on Stochastic Partial Differential Equations. Springer Verlag. Published, 12/04/2008.
  • Méndez-Hernández, Pedro J., Khoshnevisan, Davar & Levin, David A. (2008). Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov’s -entropy. Elsevier BV. Vol. 118(10), 1723-1737. Published, 2008.
  • Khoshnevisan, Davar & Nualart, Eulalia (2008). Level sets of the stochastic wave equation driven by a symmetric Lévy noise. Bernoulli Society for Mathematical Statistics and Probability. Vol. 14(4), 899-925. Published, 2008.
  • Khoshnevisan, Davar & Xiao, Yimin (2008). Packing dimension of the range of a Lévy process. American Mathematical Society (AMS). Vol. 136(07), 2597-2607. Published, 2008.
  • XIAO, YIMIN & KHOSHNEVISAN, DAVAR (2008). Packing-dimension profiles and fractional Brownian motion. Cambridge University Press (CUP). Vol. 145(01). Published, 2008.
  • Méndez-Hernández, Pedro J., Khoshnevisan, Davar & Levin, David A. (2008). Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov’s -entropy. Elsevier BV. Vol. 118(10), 1723-1737. Published, 2008.
  • Khoshnevisan, Davar & Nualart, Eulalia (2008). Level sets of the stochastic wave equation driven by a symmetric Lévy noise. Bernoulli Society for Mathematical Statistics and Probability. Vol. 14(4), 899-925. Published, 2008.
  • XIAO, YIMIN & KHOSHNEVISAN, DAVAR (2008). Packing-dimension profiles and fractional Brownian motion. Cambridge University Press (CUP). Vol. 145(01). Published, 2008.
  • Khoshnevisan, Davar & Xiao, Yimin (2008). Packing dimension of the range of a Lévy process. American Mathematical Society (AMS). Vol. 136(07), 2597-2607. Published, 2008.
  • Hausdorff dimension of the contours of symmetric additive Levy processes (with Narn-Rueih Shieh and Yimin Xiao). Probability Theory and Related Fields 140(1-2), 169-193. Published, 2008.
  • Dynamical percolation on general trees. Probability Theory and Related Fields 140(1-2), 129-167. Published, 2008.
  • Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov's epsilon-entropy (with David A. Levin and Pedro J. Mendez-Hernandez) Stochastic Proc. Appl. 118 no. 10, 1723--1737. Published, 2008.
  • Packing-dimension profiles and fractional Brownian motion. (with Yimin Xiao) The Math. Proc. Cambridge Phil. Soc. 145, no. 1, 205-213. Published, 2008.
  • Level sets of the stochastic wave equation driven by a symmetric Levy noise. (with Eulalia Nualart) Bernoulli 14, 899-925. Published, 2008.
  • Slices of the Brownian sheet: New results and open problems. Stochastic Analysis, Random Fields, and Applications V. Progress in Probability 59, 135-174, Birkhauser Verlag 2007, Basel. Published, 2008.
  • Packing dimension of the range of a Levy process. (with Yimin Xiao) The Proceedings of the AMS, Vol. 136, No. 7, 2597-2607. Published, 2008.
  • A Minicourse on Stochastic Partial Differential Equations Springer-Verlag, Berlin (2008); (editor and chapter author; coeditor: Firas Rassoul-Agha; coauthors: Robert Dalang; Carl Mueller; David Nualart; and Yimin Xiao). Published, 2008.
  • Khoshnevisan, Davar (2007). Dynamical percolation on general trees. Springer Science + Business Media. Vol. 140(1-2), 169-193. Published, 2007.
  • Khoshnevisan, Davar, Shieh, Narn-Rueih & Xiao, Yimin (2007). Hausdorff dimension of the contours of symmetric additive Lévy processes. Springer Science + Business Media. Vol. 140(1-2), 129-167. Published, 2007.
  • Zitikis, Ricardas, Davydov, Youri, Shi, Zhan & Khoshnevisan, Davar (2007). Convex rearrangements, generalized Lorenz curves, and correlated Gaussian data. Elsevier BV. Vol. 137(3), 915-934. Published, 2007.
  • Xiao, Yimin & Khoshnevisan, Davar (2007). Images of the Brownian sheet. American Mathematical Society (AMS). Vol. 359(07), 3125-3152. Published, 2007.
  • Khoshnevisan, Davar (2007). Dynamical percolation on general trees. Springer Science + Business Media. Vol. 140(1-2), 169-193. Published, 2007.
  • Zitikis, Ricardas, Davydov, Youri, Shi, Zhan & Khoshnevisan, Davar (2007). Convex rearrangements, generalized Lorenz curves, and correlated Gaussian data. Elsevier BV. Vol. 137(3), 915-934. Published, 2007.
  • Xiao, Yimin & Khoshnevisan, Davar (2007). Images of the Brownian sheet. American Mathematical Society (AMS). Vol. 359(07), 3125-3152. Published, 2007.
  • Khoshnevisan, Davar (2007). Probability. Amer Mathematical Society. Published, 04/30/2007.
  • Khoshnevisan, Davar (2007). Probability. Amer Mathematical Society. Published, 04/30/2007.
  • Probability. American Mathematical Society, Providence, Rhode Island (2007). Published, 03/20/2007.
    http://www.ams.org/publications/authors/books/post...
  • Hitting probabilities for systems of nonlinear stochastic heat equations with additive noise (with Robert C. Dalang and Eulalia Nualart) ALEA, Vol. III, 231-371. Published, 2007.
  • Convex rearrangements, generalized Lorenz curves, and correlated Gaussian data (with Y. Davydov, Z. Shi, and R. Zitikis). The J. of Statistical Planning and Inference 137, 915-934. Published, 2007.
  • Images of the Brownian sheet (with Yimin Xiao). The Transactions of the AMS, Vol. 359, No. 7, 3125-3151. Published, 2007.
  • Yor, Marc, Salminen, Paavo & Khoshnevisan, Davar (2006). A note on a.s. finiteness of perpetual integral functionals of difusions. Institute of Mathematical Statistics. Vol. 11(0). Published, 2006.
  • Khoshnevisan, Davar, Levin, David A. & Méndez-Hernández, Pedro J. (2006). Exceptional times and invariance for dynamical random walks. Springer Science + Business Media. Vol. 134(3), 383-416. Published, 2006.
  • Khoshnevisan, Davar, Levin, David A. & Méndez-Hernández, Pedro J. (2006). Exceptional times and invariance for dynamical random walks. Springer Science + Business Media. Vol. 134(3), 383-416. Published, 2006.
  • Khoshnevisan, Davar, Xiao, Yimin & Wu, Dongsheng (2006). Sectorial Local Non-Determinism and the Geometry of the Brownian Sheet. Institute of Mathematical Statistics. Vol. 11(0). Published, 2006.
  • Yor, Marc, Salminen, Paavo & Khoshnevisan, Davar (2006). A note on a.s. finiteness of perpetual integral functionals of difusions. Institute of Mathematical Statistics. Vol. 11(0). Published, 2006.
  • Khoshnevisan, Davar, Xiao, Yimin & Wu, Dongsheng (2006). Sectorial Local Non-Determinism and the Geometry of the Brownian Sheet. Institute of Mathematical Statistics. Vol. 11(0). Published, 2006.
  • Exceptional times and invariance for dynamical random walks (with David Asher Levin and Pedro J. Mendez-Hernandez). Probab. Th. Rel. Fields 134(3), 383-416. Published, 2006.
  • A note on a.s. finiteness of perpetual integral functionals of diffusions (with Paavo Salminen and Marc Yor), Electr. Comm. Probab., Vol. 11, Paper 11, pp. 108-117. Published, 2006.
  • Sectorial local non-determinism and the geometry of the Brownian sheet (with Dongsheng Wu and Yimin Xiao). Electr. J. Probab., Vol. 11, Paper 33, pp. 817-843. Published, 2006.
  • Khoshnevisan, Davar, Shi, Zhan & Levin, David A. (2005). An Extreme-Value Analysis of the LIL for Brownian Motion. Institute of Mathematical Statistics. Vol. 10(0). Published, 2005.
  • Shi, Zhan, Khoshnevisan, Davar & Révész, Pál (2005). Level crossings of a two-parameter random walk. Elsevier BV. Vol. 115(3), 359-380. Published, 2005.
  • Khoshnevisan, Davar & Xiao, Yimin (2005). Lévy processes: Capacity and Hausdorff dimension. Institute of Mathematical Statistics. Vol. 33(3), 841-878. Published, 2005.
  • Levin, David A., Khoshnevisan, Davar & Méndez-Hernández, Pedro J. (2005). On dynamical Gaussian random walks. Institute of Mathematical Statistics. Vol. 33(4), 1452-1478. Published, 2005.
  • Khoshnevisan, Davar, Shi, Zhan & Levin, David A. (2005). An Extreme-Value Analysis of the LIL for Brownian Motion. Institute of Mathematical Statistics. Vol. 10(0). Published, 2005.
  • Shi, Zhan, Khoshnevisan, Davar & Révész, Pál (2005). Level crossings of a two-parameter random walk. Elsevier BV. Vol. 115(3), 359-380. Published, 2005.
  • Khoshnevisan, Davar & Xiao, Yimin (2005). Lévy processes: Capacity and Hausdorff dimension. Institute of Mathematical Statistics. Vol. 33(3), 841-878. Published, 2005.
  • Levin, David A., Khoshnevisan, Davar & Méndez-Hernández, Pedro J. (2005). On dynamical Gaussian random walks. Institute of Mathematical Statistics. Vol. 33(4), 1452-1478. Published, 2005.
  • Level crossings of a two-parameter random walk, (With P. Revesz, and Z. Shi) Stoch. Proc. Their Appl. 115, 359-380. Published, 2005.
  • Levy processes: capacity, and Hausdorff dimension (With Yimin Xiao) Ann. Probab. 33(3), 841-878. Published, 2005.
  • On dynamical Gaussian random walks (with David Asher Levin and Pedro J. Mendez-Hernandez) Ann. Probab. 33(4), 1452-1478. Published, 2005.
  • An extreme-value analysis of the LIL for Brownian motion (with David A. Levin and Zhan Shi) Electr. Comm. Probab., Vol. 10, Paper 20, pp. 196-206. Published, 2005.
  • Dalang, Robert C. & Khoshnevisan, Davar (2004). Recurrent lines in two-parameter isotropic stable Lévy sheets. Elsevier BV. Vol. 114(1), 81-107. Published, 2004.
  • KHOSHNEVISAN, D (2004). On the explosion of the local times along lines of Brownian sheet. Institute of Mathematical Statistics. Vol. 40(1), 1-24. Published, 2004.
  • Khoshnevisan, D (2004). On the explosion of the local times along lines of Brownian sheet. Institute of Mathematical Statistics. Vol. 40(1), 1-24. Published, 2004.
  • Khoshnevisan, D (2004). On the explosion of the local times along lines of Brownian sheet. Institute of Mathematical Statistics. Vol. 40(1), 1-24. Published, 2004.
  • KHOSHNEVISAN, D (2004). On the explosion of the local times along lines of Brownian sheet. Institute of Mathematical Statistics. Vol. 40(1), 1-24. Published, 2004.
  • Dalang, Robert C. & Khoshnevisan, Davar (2004). Recurrent lines in two-parameter isotropic stable Lévy sheets. Elsevier BV. Vol. 114(1), 81-107. Published, 2004.
  • Recurrent lines in two-parameter isotropic stable stable sheets, (with R. C. Dalang) Stoch. Proc. Appl. 114, 81-107. Published, 2004.
  • Brownian sheet and quasi-sure analysis, Fields Inst. Comm. Vol. 44, 25--47. Published, 2004.
  • On the explosion of local times of Brownian sheet along lines, (with P. Revesz and Z. Shi) Ann. IHP. 40(1), 1-24. Published, 2004.
  • Additive Levy processes: Capacity and dimension, (with Yimin Xiao) Progress in Probab. Vol. 57, 151-170. Published, 2004.
  • The codimension of the zeros of a stable process in random scenery. Sem. de Probab. XXXVII Lecture Notes in Math. 1832, 236-245. Published, 2003.
  • Weak unimodality of finite measures, and an application to potential theory of additive Levy processes. (with Y. Xiao) The Proceedings of the AMS, 131(8), 2611-2616. Published, 2003.
  • Local times of additive Levy processes (with Y. Xiao and Y. Zhong) Stoch. Proc. Their Appl., 104, 193-216. Published, 2003.
  • Intersections of Brownian motions, Expos. Math., 21(2), 97-114. Published, 2003.
  • Measuring the range of an additive Levy process (with Y. Xiao and Y. Zhong), Ann. Probab. 31(2), 1097-1141. Published, 2003.
  • Optimal reward on a sparse tree with random edge-weights, (with T. M. Lewis) J. of Applied Probab., Vol. 40(4), 926-945. Published, 2003.
  • Bounds on gambler's ruin probabilities in terms of moments (w/ S. N. Ethier) Methodology and Computing in Applied Probab., 4(1), 55-68. Published, 2002.
  • Level sets of additive Levy processes (w/ Y. Xiao) Ann. Probab., 30(1), 62-100. Published, 2002.
  • On the most visited sites of symmetric Markov processes. (w/ N. Eisenbaum) Stoch. Proc. and Their Appl., 101, 241-256. Published, 2002.
  • Multiparameter Processes: An Introduction to Random Fields Springer, New York (2002). Published, 2002.
  • Fast sets and points for fractional Brownian motion (w/ Z. Shi) Seminaire de Probab. XXXIV, Lec. Notes in Math., 393-416. Published, 2000.
  • Boundary crossings and the distribution function of the maximum of Brownian sheet (w/ E. Csaki and Z. Shi), Stoch. Proc. Their Appl., 90, 1-18. Published, 2000.
  • Sojourn times of Brownian sheet (w/ R. Pemantle) Periodica Math. Hung., 41(1-2), 187-194. Published, 2000.
  • On sums of iid random variables indexed by N parameters Seminaire de Probab. XXXIV, Lec. Notes in Math., 151-156. Published, 2000.
  • Images and level sets of additive random walks (w/ Y. Xiao), In: High-dimensional Probab. II, 329-346, Birkhauser, Boston, (Seattle, 1999; Ed's: E. Gine, D. M. Mason, J. A. Wellner). Published, 2000.
  • Limsup random fractals (w/ Y. Peres and Y. Xiao) Elec. J. Probab., 5(4), 1-24. Published, 2000.
  • Brownian sheet and capacity (w/ Z. Shi) Ann. Probab., 27, 1135-1159. Published, 1999.
  • Capacity estimates, boundary crossings and the Ornstein-Uhlenbeck process in Wiener space (w/ E. Csaki and Z. Shi), Elec. Comm. Probab., 4(13), 103-109. Published, 1999.
  • Stochastic calculus for Brownian motion on a Brownian fracture (w/ T. M. Lewis) Ann. Applied Probab., 9, 629-667. Published, 1999.
  • Brownian sheet images and Bessel-Riesz capacity Trans. Amer. Math. Soc. 351(7), 2607-2622. Published, 1999.
  • Iterated Brownian motion and its intrinsic skeletal structure (w/ T. M. Lewis) Progress in Probab.,45, 201-210, Birkhauser-Verlag, Basel. Published, 1999.
  • Brownian motion in a Brownian crack (w/ K. Burdzy) Ann. Applied Probab., 8(3), 708-748. Published, 1998.
  • Chung's law for integrated Brownian motion (w/ Z. Shi) Trans. Amer. Math. Soc., 350(10), 4253-4246. Published, 1998.
  • A law of the iterated logarithm for stable processes in random scenary (w/ T. M. Lewis) Stoch. Proc. Their Appl., 74, 89-121. Published, 1998.
  • Gaussian measure of a small ball and capacity in Wiener space (w/ Z. Shi), Asymptotic Methods in Probab. Statist., 453-465, Elsevier Science, Am. Published, 1998.
  • Logarithmic averages of stable random variables are asymptotically normal (w/ I. Berkes and L. Horvath), Stoch. Proc. Their Appl., 77, 35-51. Published, 1998.

Research Keywords

  • Probability theory, stochastic processes

Grants, Contracts & Research Gifts

  • Conference Proposal: Frontier Probability Days 2014 (1407136). PI: Sunder Sethuraman. Co-PI(s): DAVAR KHOSHNEVISAN. National Science Foundation, 2014 - 02/28/2015. Total project budget to date: $20,000.00
  • Intermittency and Random Fractals (1307470). PI: Davar Khoshnevisan. National Science Foundation, 2013 - 07/31/2016. Total project budget to date: $399,245.00
  • Support for the US participants of the 6th Levy Conference; Technical University of Dresden, Germany; July 2010 (1007460). PI: Rosinski, Jan. Co-PI(s): DAVAR KHOSHNEVISAN. National Science Foundation, 2010 - 04/30/2011. Total project budget to date: $15,000.00
  • Geometry of Random Fields and Stochastic Partial Differential Equations (1006903). PI: Khoshnevisan, Davar. National Science Foundation, 2010 - 07/31/2013. Total project budget to date: $411,203.00
  • Support for the US participants of the 6th Levy Conference; Technical University of Dresden, Germany; July 2010 (1007460). PI: Rosinski, Jan. Co-PI(s): DAVAR KHOSHNEVISAN. National Science Foundation, 2010 - 04/30/2011. Total project budget to date: $15,000.00
  • MSPA-MCS: High-Dimensional, Nonparametric Density Estimation for the Analysis of Images and Shapes (0732227). PI: Whitaker, Ross. Co-PI(s): DAVAR KHOSHNEVISAN. National Science Foundation, 2008 - 12/31/2011. Total project budget to date: $474,000.00
  • Random Fields and Stochastic Partial Differential Equations (0706728). PI: Khoshnevisan, Davar. National Science Foundation, 2007 - 06/30/2011. Total project budget to date: $414,854.00
  • Random Fields and Stochastic Partial Differential Equations (0706728). PI: Khoshnevisan, Davar. National Science Foundation, 2007 - 06/30/2011. Total project budget to date: $414,854.00
  • New Perspectives on Random Fields with Applications (0404729). PI: Khoshnevisan, Davar. National Science Foundation, 2004 - 07/31/2008. Total project budget to date: $295,162.00
  • New Perspectives on Random Fields with Applications (0404729). PI: Khoshnevisan, Davar. National Science Foundation, 2004 - 07/31/2008. Total project budget to date: $295,162.00
  • New Perspectives on Random Fields with Applications (0404729). PI: Khoshnevisan, Davar. National Science Foundation, 2004 - 07/31/2008. Total project budget to date: $295,162.00
  • Analytic and Geometric Properties of Random Fields (0103939). PI: Khoshnevisan, Davar. National Science Foundation, 2001 - 07/31/2005. Total project budget to date: $203,937.00
  • Analytic and Geometric Properties of Random Fields (0103939). PI: Khoshnevisan, Davar. National Science Foundation, 2001 - 07/31/2005. Total project budget to date: $203,937.00
  • Analytic and Geometric Properties of Random Fields (0103939). PI: Khoshnevisan, Davar. National Science Foundation, 2001 - 07/31/2005. Total project budget to date: $203,937.00