Exponential Mixing for Retarded Stochastic Differential Equations
Probability
2013-06-18 v1
Abstract
In this paper, we discuss exponential mixing property for Markovian semigroups generated by segment processes associated with several class of retarded Stochastic Differential Equations (SDEs) which cover SDEs with constant/variable/distributed time-lags. In particular, we investigate the exponential mixing property for (a) non-autonomous retarded SDEs by the Arzel\`{a}--Ascoli tightness characterization of the space equipped with the uniform topology (b) neutral SDEs with continuous sample paths by a generalized Razumikhin-type argument and a stability-in-distribution approach and (c) jump-diffusion retarded SDEs by the Kurtz criterion of tightness for the space endowed with the Skorohod topology.
Cite
@article{arxiv.1306.3585,
title = {Exponential Mixing for Retarded Stochastic Differential Equations},
author = {Jianhai Bao and George Yin and Leyi Wang and Chenggui Yuan},
journal= {arXiv preprint arXiv:1306.3585},
year = {2013}
}
Comments
20 pages