The Stochastic Heat Equation Driven by a Gaussian Noise: germ Markov Property

Abstract

Let $u=\{u(t,x);t\in [0,T],x\in {\mathbb{R}}^d\}$ be the process solution of the stochastic heat equation $u_t=\Delta u+\dot{F},u(0,\cdot )=0$ driven by a Gaussian noise $\dot{F}$, which is white in time and has spatial covariance induced by the kernel $f$. In this paper we prove that the process $u$ is locally germ Markov, if $f$ is the Bessel kernel of order $α=2k,k \in \bN_{+}$, or $f$ is the Riesz kernel of order $α=4k,k \in \bN_{+}$.

20 pages

Cited by in corpus (1)

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