arXiv Analytics

Sign in

arXiv:1905.04843 [math.PR]AbstractReferencesReviewsResources

Periodic solutions of stochastic differential equations driven by Lévy noises

Xiao-Xia Guo, Wei Sun

Published 2019-05-13Version 1

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.

Categories: math.PR
Subjects: 60H10, 60J75, 34C25, 37B25
Related articles: Most relevant | Search more
arXiv:1205.6115 [math.PR] (Published 2012-05-28)
First exit times of solutions of stochastic differential equations driven by multiplicative Levy noise with heavy tails
arXiv:math/0304134 [math.PR] (Published 2003-04-10, updated 2004-03-09)
Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion
arXiv:1408.4377 [math.PR] (Published 2014-08-19)
A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion

Links

Toolbox