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- Title
Space-time fractional Anderson model driven by Gaussian noise rough in space.
- Authors
Liu, Junfeng; Wang, Zhi; Wang, Zengwu
- Abstract
In this paper, we study a class of space-time fractional Anderson model driven by multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst index H < 1 2 in space. We prove the existence of the solution in the Skorohod sense and obtain the upper and lower bounds for the p th moments for all p ≥ 2. Then we can prove that solution of this equation in the Skorohod sense is weakly intermittent. We also deduce the Hölder continuity of the solution with respect to the time and space variables.
- Subjects
ANDERSON model; RANDOM noise theory; SPACETIME; BROWNIAN motion; UNDERWATER noise; MALLIAVIN calculus; NOISE
- Publication
Stochastics & Dynamics, 2023, Vol 23, Issue 1, p1
- ISSN
0219-4937
- Publication type
Article
- DOI
10.1142/S021949372350003X