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Strong averaging principle for slow-fast SPDEs with Poisson random measures. (English) Zbl 1335.60118
Summary: 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.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G57 Random measures
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F15 Strong limit theorems
70K65 Averaging of perturbations for nonlinear problems in mechanics
70K70 Systems with slow and fast motions for nonlinear problems in mechanics
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