L^p-strong convergence of the averaging principle for slow-fast SPDEs with jumps

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• 作者：Jie Xu ^{xujiescu@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Stochastic averaging principle with jumps ; LpLp-strong convergence ; Fast&ndash ; slow SPDEs
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：342-373
• 全文大小：515 K

文摘

The averaging principle is an important method to extract effective macroscopic dynamic from complex systems with slow component and fast component. This paper concerns the L^p$L^p$-strong convergence of the averaging principle for two-time-scales stochastic partial differential equations (SPDEs) driven by Wiener processes and Poisson jumps. To achieve this, a key step is to show the existence for an invariant measure with exponentially ergodic property for the fast equation, where the dissipative conditions are needed. Furthermore, it is shown that under suitable assumptions the slow component L^p$L^p$-strongly converges to the solution of the averaged equation. The rate of the convergence is also obtained as a byproduct.