Periodic solutions of stochastic differential equations driven by Levy noises

Xiao-Xia Guo; Wei Sun

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arXiv · 1905.04843

Periodic solutions of stochastic differential equations driven by Levy noises

Xiao-Xia Guo·Wei Sun

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Abstract

In this paper, we first show the well-posedness of the SDEs driven by L\'{e}vy noises under mild conditions. Then, we consider the existence and uniqueness of periodic solutions of the SDEs. To establish the ergodicity and uniqueness of periodic solutions, we investigate the strong Feller property and the irreducibility of the corresponding time-inhomogeneous semigroups when both small and large jumps are allowed in the equations. Some examples are presented to illustrate our results.

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Xiao-Xia Guo, Wei Sun. 2019-05-13. Periodic solutions of stochastic differential equations driven by Levy noises. https://arxiv.org/abs/1905.04843

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