Strong averaging principle for slow-fast SPDEs with Poisson random measures

By Jie Xu, Y. Miao, Jicheng Liu. 2015

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This work concerns the problem associated with an averaging principle for two-time-scales stochastic partial differential equations (SPDEs) driven by cylindrical Wiener processes and Poisson random measures. Under suitable dissipativity conditions, the existence of an averaging equation eliminating the fast variable for the coupled system is proved, and as a consequence, the system can be reduced to a single SPDE with a modified coefficient. Moreover, it is shown that the slow component mean-square strongly converges to the solution of the corresponding averaging equation.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/2cb92f3a05e21e8a8d7a97547116544ea6e537c4