Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise

AIMS Mathematics

卷:6

Yan Wang¹  Xin Liu¹ 

[1] School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;

关键词: averaging principle;    stochastic differential equations;    lévy noise;    periodic solution;    quasi-periodic solution;    almost periodic solution;    poisson stable solution;   

DOI  :  10.3934/math.2021314

来源: DOAJ

【 摘 要 】

In this paper, we establish an averaging principle on the infinite time intervals for semilinear stochastic ordinary differential equations with Lévy noise. In particular, under suitable conditions we prove that if the coefficients are Poisson stable (including periodic, quasi-periodic, almost periodic, almost automorphic etc), then there exists a unique L²-bounded solution of the original equation, which inherits the recurrence property of the coefficients, and the recurrent solution uniformly converges to the stationary solution of the averaged equation on the whole real axis in distribution sense.

【 授权许可】

Unknown