期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
卷 25, 期 3, 页码 1141-1158出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2019213
关键词
Averaging principle; mild solution; fractional Brownian motion; fast-slow; stochastic partial differential equations
资金
- NSF of China [11802216, 11702216]
- China Postdoctoral Science Foundation [2019M651334]
- JSPS KAKENHI [JP18F18314]
- Shaanxi Province Project for Distinguished Young Scholars
- Fundamental Research Funds for the Central Universities
- JSPS for Postdoctoral Fellowships for Research in Japan
In this paper, we focus on fast-slow stochastic partial differential equations in which the slow variable is driven by a fractional Brownian motion and the fast variable is driven by an additive Brownian motion. We establish an averaging principle in which the fast-varying diffusion process will be averaged out with respect to its stationary measure in the limit process. It is shown that the slow-varying process L-p(p >= 2) converges to the solution of the corresponding averaging equation. To reduce the complexity, one can concentrate on the limit process instead of studying the original full fast-slow system.
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