Year: 2024
Type: article
Abstract: In this article, we consider the stochastic fractional diffusion equation ∂β+ ν2 −Δα∕2u(t,x)=λI0+γu(t,x)W˙(t,x),t>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.
Source: Bernoulli
DOI: 10.3150/23-bej1652
Authors: Yuhui Guo, Jian Song, Xiaoming Song
Institutions: Shandong University, Drexel University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4396943316