Small ball probabilities for the stochastic heat equation with colored noise

Jiaming Chen

Stochastic Processes and their Applications, 2024, vol. 177, issue C

Abstract: We consider the stochastic heat equation on the 1-dimensional torus T≔−1,1 with periodic boundary conditions: ∂tu(t,x)=∂x2u(t,x)+σ(t,x,u)Ḟ(t,x),x∈T,t∈R+,where Ḟ(t,x) is a generalized Gaussian noise, which is white in time but colored in space. Assuming that σ is Lipschitz in u and uniformly bounded, we estimate small ball probabilities for the solution u when u(0,x)≡0.

Keywords: Stochastic heat equation; Colored noise; Small ball probabilities (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104455

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