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Strong convergence in the \(p\)th-mean of an averaging principle for two-time-scales SPDEs with jumps. (English) Zbl 1422.60113

Summary: The main goal of this work is to study an averaging principle for two-time-scales stochastic partial differential equations with jumps. The solutions of reduced equations with modified coefficients are derived to approximate the slow component of the original equation under suitable conditions. It is shown that the slow component can strongly converge to the solution of the corresponding reduced equation in the \(p\)th-mean. Our key and novel idea is how to cope with the changes caused by jumps and higher order moments.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
60J75 Jump processes (MSC2010)
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