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We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...
We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...
Let xi(t, x) denote space-time white noise and consider a reaction-diffusion equation of the form (t, x) = 1/2u ''(t, x) + b(u(t, x)) + sigma(u(t,x))xi(t,x) on R+ x [0, 1], with homogeneous Dirichlet boundary conditions and suitable initial d ...
We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...
We consider a system of d non-linear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative d-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point probability density function of ...
We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, partial derivative/partial derivative t u(t, x) = partial derivative(2)/partial derivative x(2) u(t, x) + sigma (u(t, ...
We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...
We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify con ...
We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix gamma z of Z := (u(s, y), u(t , x) - u(s, y)), where u is the solution to a system of d non-linear stochastic heat equations in spatial dimension k >= ...
This article discusses the life and work of Professor Srishti Dhar Chatterji, who passed away on September 28, 2017, in Lausanne, Switzerland, most suddenly and unexpectedly, after a very brief illness. Complete bibliographical information is included. (C) ...
