Journal article
Stochastic fractional diffusion equations with Gaussian noise rough in space
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, v 30(3), pp 1774-1799
01 Aug 2024
Abstract
In this article, we consider the stochastic fractional diffusion equation (partial derivative(beta) + nu/2 (-Delta)(alpha/2) ) u(t , x ) = lambda I-0+(y) [u(t , x )W(t , x )] , t > 0 , x is an element of R, where alpha > 0, beta is an element of (0 , 2 ], gamma >= 0, lambda # 0, nu > 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 Ito-Skorohod sense and obtain the lower and upper bounds for the p-th moment. The H & ouml;lder regularity of the solution is also studied.
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Details
- Title
- Stochastic fractional diffusion equations with Gaussian noise rough in space
- Creators
- Yuhui Guo - Shandong UniversityJian Song - Shandong UniversityXiaoming Song - Drexel University
- Publication Details
- Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, v 30(3), pp 1774-1799
- Publisher
- Int Statistical Inst
- Number of pages
- 26
- Grant note
- 12071256 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC) ZR2019ZD42; ZR2020ZD24 / Major Basic Research Program of the Natural Science Foundation of Shandong Province in China
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001406618300004
- Scopus ID
- 2-s2.0-85194382173
- Other Identifier
- 991022202495404721