### AIMS Mathematics

2021, Issue 5: 5316-5350. doi: 10.3934/math.2021314
Research article

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

• Received: 16 January 2021 Accepted: 03 March 2021 Published: 12 March 2021
• MSC : 34C29, 60H10, 60G51, 37B20, 34C27

• 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 $\mathcal L^2$-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.

Citation: Xin Liu, Yan Wang. Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise[J]. AIMS Mathematics, 2021, 6(5): 5316-5350. doi: 10.3934/math.2021314

### Related Papers:

• 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 $\mathcal L^2$-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.

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