On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise

Bin Zhang, Zhigang Yao and Junfeng Liu

Statistics & Probability Letters, 2023, vol. 196, issue C

Abstract: In this paper, we study a class of nonlinear stochastic heat equations ∂∂tu(t,x)=Δ+aαΔα2+b⋅∇u(t,x)+σ(u(t,x))Ẇ(t,x), where Ẇ denotes the Gaussian noise which is white in time and spatially homogeneous in space. The existence, uniqueness and the Hölder continuity of the mild solution to the above equation are proved.

Keywords: Mixed stochastic heat equation; Spatially homogeneous Gaussian noise; Riesz kernel; Hölder continuity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109807

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