To Appear
(with S. Athreya and M. Joseph) Sausage volume of the random string and survival in a medium of poisson traps, Ann. Inst. Poincare.
Published
(with E. Neuman) Scaling Properties of Star Polymers in Three or More Dimension, J. of Stat. Phys., 192 article no. 68, (27 pp.) (2025).
D. Khoshnevisan and K. Kim) Small-ball constants, and exceptional flat points of SPDEs, Electronic J. Probab., 29, paper no. 180, 1-31 (2024).
(with D. Khoshnevisan and K. Kim) On the Valleys of the Stochastic Heat Equation, Ann. Appl. Probab. 34, 1B, 1177–1198 (2024)
(with L. Chen, S. Kuzgun and P. Xia) On the radius of self-repellent fractional Brownian motion, J. Stat. Phys., 191, 19 (2024).
(with D. Khoshnevisan and K. Kim) Dissipation in Parabolic SPDEs II: Oscillation and decay of the solution, Ann. Inst. Henri Poincare, 59, 3, 1610-1641 (2023).
(with D. Khoshnevisan, K. Kim, and S-Y Shiu) Phase analysis for a family of stochastic reaction-diffusion equations, Electronic J. Probab., 28, 1-66 (2023).
(with E. Neuman) The effective radius of self repelling elastic manifolds, Ann. Appl. Prob., 33, 6B, 5668-5692 (2023).
(with E. Neuman) Self-repelling elastic manifolds with low dimensional range, J. Stoch. Analysis 3, 2, 1-16 (2022).
(with E. Neuman) Scaling properties of a moving polymer, Ann. Appl. Probab. 32, 6, 4251-4278 (2022).
(with L. Mytnik and L. Ryzhik) The speed of a random front for stochastic reaction-diffusion equations with strong noise, Comm. Math. Phys. 384, 699–732 (2021).
(with R. Dalang and Y. Xiao) Polarity of almost all points for systems of non-linear stochastic heat equations in the critical dimension, Ann. Probab. 49, 5, 2573-2598 (2021).
(with S. Athreya and M. Joseph) Small ball and support theorems for SPDE, Ann. Probab. 49, 5, 2548-2572 (2021).
(with R. Dalang, C-Y Lee, and Y. Xiao) Multiple points of Gaussian random fields, Electronic J. Probab., 26, paper no. 17, 1-25 (2021).
(with G. Truong) Uniqueness of a three-dimensional stochastic differential equation, Involve, 13, 3, 433-444 (2020).
(with Eyal Neuman, Michael Salins, and Giang Truong) An Improved Uniqueness Result for a system of SDE Related to the stochastic wave equation, Journal of Stochastic Analysis, 1, 2, article 1 (2020).
(with D. Khoshnevisan, K. Kim, and S-Y Shiu) Dissipation in parabolic SPDEs, J. Stat. Phys. 179, 2, 502-534 (2020).
(with J. J. Lee and E. Neuman) Hitting probabilities of a Brownian flow with Radial Drift, Ann. Probab. 48, 2, 646-671 (2020).
(with K. Lin) Can the Stochastic Wave Equation with Strong Drift Hit Zero?, Electronic Journal of Probability 24, paper 14, 1-26 (2019).
(with A. Gomez, J. J. Lee, E. Neuman, and M. Salins) On uniqueness and blowup properties for a class of second order SDEs, Electronic Journal of Probability 22, 1-17 (2017).
(with L. Mytnik and E. Perkins) On the boundary of the support of super-Brownian motion, Ann. Probab. 45, Number 6A, 3481-3534 (2017).
(with D. Khoshnevisan and M. Joseph) Strong invariance and noise comparison principles for some parabolic SPDEs, Ann. Probab. 45, Number 1, 377-403 (2017).
(with R. Dalang and Y. Xiao) Polarity of points for Gaussian random fields, Ann. Probab. 45, Number 6B (November 2017), 4700-4751 (2017).
Lecture notes on SPDE from the point of view of particle systems and duality, in Stochastic Analysis: A Series of Lectures, Birkhauser, Progress in Probability, 68, 271-295 (2015)
(with R. Dalang) Multiple points of the Brownian sheet in critical dimensions, Ann. Probab. 43, 4, 1577-1593 (2015).
(with G. Richards) Can solutions of the one-dimensional wave equation with nonlinear multiplicative noise blow up?, Open Prob. Math 2, 1-4 (2014).
(with L. Mytnik and E. Perkins) Nonuniqueness for a parabolic SPDE with 3/4-epsilon Holder diffusion coefficients, Ann. Probab. 42, 5, 2032-2112 (2014).
(with S. Starr) The length of the longest increasing subsequence of a random Mallows permutation, J. of Th. Probab. 26, 2, 514-540 (2013).
(with A. Wei, A. Gomez, K. Lee, and J. Xiong) Strong uniqueness for an SPDE via backward doubly stochastic differential equations, Stat. and Probab. Letters 83, 2186-2190 (2013).
(with L. Mytnik and J. Quastel) Effect of noise on front propagation in reaction-diffusion equations of KPP type, Invent. Math. 184, 2, 405-453 (2011).
(With R. Tribe) A phase diagram for a stochastic reaction diffusion system, Probab. Th. Rel. Fields, 149, 3-4, 561-637 (2011).
(with K. Kim and R. Sowers) A stochastic moving boundary value problem, Ill. J. Math., 54, 3, 927-962 (2010).
(with K. Burdzy and E. Perkins) Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations, Ill. J. Math., 54, 4, 1481-1507 (2010).
(With Y. Bakhtin) Solutions of semilinear wave equation via stochastic cascades, Comm. Stoch. Anal., 4, 3, 425-431 (2010).
(with K. Lee and J. Xiong) Some properties for superprocess under a stochastic flow, Ann. Inst. Poincare, 45, 2, 477-490 (2009).
(with R. Dalang) Intermittency properties in a hyperbolic Anderson model, Ann. Inst. Henri Poincare, 45, 4, 1150-1164 (2009).
(with K. Lee) On the discrete heat equation taking values on a tree, Proc. Amer. Math. Soc., 137, 1467-1478, (2009).
Some tools and results for parabolic stochastic partial differential equations, in Proceedings of a summer school in probability, University of Utah, Editors Davar Khoshnevisan and Firas Rassoul-Agha, Lecture Notes in Mathematics number 1962, Springer, p. 111-144 (2009).
(with Z. Wu) A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand, Electronic Comm. Probab., 14, 55-65, (2009).
(with L. Mytnik and J. Quastel) Small noise asymptotics of traveling waves, Markov Proc. Rel. Fields, 14, 3, 333-342, (2008).
(with D. Nualart) Regularity of the density for the stochastic heat equation, Electronic J. Probab., 13, paper 74, 2248-2258, (2008).
(with R. Dalang and R. Tribe) A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s, Trans. Amer. Math. Soc. 360, 9, 4681-4703, (2008).
(with K. Fleischmann and P. Vogt) On the large scale behavior of superbrownian motion with a single point source, Comm. Stoch. Anal., 1, 1, 19-28, (2007).
(with R. Dalang and L. Zambotti) Hitting properties of s.p.d.e.'s with reflection, Ann. Probab., 34, 4, 1423-1450, (2006).
(with L. Mytnik and A. Stan) The heat equation with time-independent multiplicative stable L\'evy noise, Stochastic Process. Appl., 116, 1, 70-100, (2006).
(with A. Stan) A Heisenberg inequality for stochastic integrals, J. of Theoretical Probability, 18, 2, 291-315, (2005).
(with A. Stan) A stochastic Heisenberg inequality, in Quantum Information and Complexity, Proceedings of the Meijo Winter School 2003, edited by T. Hida, K. Saito, and Si Si, World Scientific, Singapore, 362-375, (2004).
(with K. Fleischmann) Super-Brownian motion with extra birth at one point, SIAM J. Math. Anal., 36, 3, 740-772, (2004).</li>
<li>(with R. Tribe) A singular parabolic Anderson model, Electronic J. Prob., 9, paper 5, 98-144, (2004).
(with C. Doering and P. Smereka) Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality, Phys. A 325, 243-259 (2003).
(with C. Doering and P. Smereka) Noisy wavefront propagation in the Fisher-Kolmogorov-Petrovsky-Piscounov equation, in UpoN 2002: Proceedings of the 3rd International Conference on Unsolved Problems of Noise, NIH, Bethesda, ed. S. Bezrukov (American Institute of Physics, 2003). (pp 523-530)
(with R. Dalang) Some non-linear s.p.d.e.'s that are second order in time, Electronic J. Probab., 8, paper 1, 1-21, (2003)</li>
<li>(with R. Tribe) Hitting properties of a random string, Electronic J. Probab., 7, paper 10, 1-29, (2002).
(with R. Tribe) A Measure-Valued Process Related to the Parabolic Anderson Model, Proceedings of a Conference at Ascona, Progress in Probability, Birkhauser, Boston, MA, (2002).
The critical parameter for the heat equation with a noise term to blow up in finite time, Ann. Probab., 28, 4, 1735-1746, (2000).
(with D. Dawson and K. Fleischmann) Finite time extinction of superprocesses with catalysts, Ann. Probab., 28, 2, 603-642, (2000).
(with E. Perkins) Extinction for two parabolic stochastic PDE's on the lattice, Ann. Inst. Henri Poincare, 36, 301-338, (2000).
(with K. Fleischmann) Finite time extinction of catalytic branching processes. Stochastic Models, Proceedings of the International Conference on Stochastic Models, Ottawa, Canada, June 10-13, 1998, edited by L.G. Gorostiza and B.G. Ivanoff, CMS Conference Proceedings, Vol. 26, AMS and CMS, Providence RI, 125-140.
(with E. Pardoux) The critical exponent for a stochastic PDE to hit zero. Stochastic analysis, control, optimization and applications, 325-338, Systems Control Found. Appl., Birkhauser, Boston, MA, (1999).
The heat equation with Levy noise, Stoch. Proc. and Appl., 74, 67-82 (1998).
Long-time existence for signed solutions of the heat equation with a noise term, Probab. Th. Rel. Fields, 110, 51-68, (1998).
(with R. Tribe) Finite width for a random stationary interface, Electronic J. Probab., 2, paper 7, 1-27, (1997).
(with K. Fleischmann) A super-Brownian motion with a locally infinite catalyst, Probab. Th. Rel. Fields, 107, 3, 325-358, (1997).
Long time existence for the wave equation with a noise term, Ann. Probab., 25, 1, 133-151 (1997).
Singular initial conditions for the heat equation with noise, Ann. Probab., 24, 1, 377-398, (1996).
(with R. Tribe) Stochastic p.d.e.'s arising from the long range contact and long range voter models, Probab. Th. Rel. Fields, 102, 4, 519-546, (1995).
(with D. Dawson and Yi Li) The support of measure-valued branching processes in a random environment, Ann. Probab., 23, 4, 1692-1718, (1995).
(with D. Dawson, K. Fleischmann and Yi Li) Singularity of super-Brownian local time at a point catalyst, Ann. Probab., 23, 37-55, (1995).
(with R. Sowers) (summary) Travelling waves for the KPP equation with noise. Proceedings of Symposia in Pure Mathematics, 57, 603-609, (1995).
(with R. Sowers) Travelling waves for the KPP equation with noise, J. Functional Anal., 128, 439-498, (1995).
(with R. Tribe) A phase transition for a stochastic PDE related to the contact process, Probab. Th. Rel. Fields, 100, 2, 131-156, (1994).
(with R. Tribe) (summary) A stochastic PDE arising as the limit of a long-range contact process, and its phase transition, Proceedings of a conference in probability at Montreal, CRM Proceed ings and Lecture Notes, vol. 5, 1994, 175-178.
(with R. Sowers) Blow-up for the heat equation with a noise term. Probab. Th. Rel. Fields., 97, 287-320, (1993).
A modulus for the 3-dimensional wave equation with noise: dealing with a singular kernel, Canadian J. Math., 45, 6, 1263-1275, (1993).
Coupling and invariant measures for the heat equation with noise term, Ann. Probab., 21, 4, 2189-2199, (1993).
(with E. Perkins) The compact support property for solutions to the heat equation with noise, Probab. Th. Rel. Fields, 93, 325-358 (1992).
Long time existence for the heat equation with a noise term, Probab. Th. and Related Fields, 90, 505-518, (1991).
On the support of solutions to the heat equation with noise, Stochastics, 37, 4, 225-246, (1991).
Limit results for two stochastic partial differential equations, Stochastics, 37, 3, 175-199, (1991).
A connection between Strassen's and Donsker-Varadhan's laws of the iterated logarithm, Probab. Th. Related Fields, 87, 365-388 (1991).
Probability and the Equivalence of Generalized Hp Spaces, Indiana U. Math. J., 38, 4 (1989).
(with Li Liu) On the extinction of measure-valued critical branching Brownian motion, Ann. of Probab. 17, (1989).
A counterexample concerning Brownian motion on manifolds. (Proceedings of a Conference on Stochastic Differential Geometry) AMS Contemporary Mathematics Series, v.73,, 217-222 (1988).
(with M. Cranston) A review of recent and older results on the absolute continuity of harmonic measure. (Proceedings of a Conference on Stochastic Differential Geometry) AMS Contemporary Mathematics Series, v.73,, 9-20 (1988).
(with F. Weissler) Single point blow-up for a nonlinear heat equation. Indiana U. Math. J., 34, 881-913 (1985).
(with S. Goldberg) Brownian motion, geometry, and generalizations of Picard's little theorem, Ann. Probab., 11, 833-846 (1983).
Strassen's law for local time, Z. Wahrsch, 63), 29-41 (1983.
(Announcement) (with S. Goldberg) Brownian motion, geometry, and generalizations of Picard's little theorem, Bull. Amer. Math. Soc., 7, 259-263 (1982).
(with F. Weissler) Hypercontractivity for the heat semigroup for ultraspherical polynomials on the n-sphere, J. Functional Analysis, (2) 48, 262-283 (1982).
Exit times of diffusions, Proceedings of the Conference on Martingale Theory, Cleveland, Springer-Verlag (1982).
A characterization of BMO and BMO_rho, Studia. Math., 72, 47-57 (1982).
A unification of Strassen's law and Levy's modulus of continuity, Z.Wahrsch., 56, 163-179 (1981).