An averaging principle for stochastic evolution equations with jumps and random time delays

Min Han; Bin Pei; Min Han; Bin Pei

doi:10.3934/math.2021003

AIMS Mathematics

2021, Volume 6, Issue 1: 39-51. doi: 10.3934/math.2021003

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Research article

An averaging principle for stochastic evolution equations with jumps and random time delays

Min Han ¹,
Bin Pei ^{2
,
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1.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710072, China
2.
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

Received: 22 July 2020 Accepted: 16 September 2020 Published: 28 September 2020
MSC : 60H15, 70K70, 34C29

This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.
- averaging principle,
- stochastic evolution equations,
- jumps,
- random time delays,
- two-time-scale Markov switching processes
Citation: Min Han, Bin Pei. An averaging principle for stochastic evolution equations with jumps and random time delays[J]. AIMS Mathematics, 2021, 6(1): 39-51. doi: 10.3934/math.2021003

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Abstract

This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.

References

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