Stochastic fractional diffusion equations with Gaussian noise rough in space

2023/03/21 by Guo, Yuhui, Song, Jian, Song, Xiaoming · 3 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2303.11939

Abstract

In this article, we consider the following stochastic fractional diffusion equation (∂^β+\dfracν2(-Δ)^{α/ 2}) u(t, x)= λ I₀₊^γ[u(t, x) W(t, x)] , tgt;0, x ∈ ℝ, where α>0, β∈(0,2], γ≥ 0, λ≠0, ν>0, and W is a Gaussian noise which is white or fractional in time and rough in space. We prove the existence and uniqueness of the solution in the Itô-Skorohod sense and obtain the lower and upper bounds for the p-th moment. The Hölder regularity of the solution is also studied.

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