English

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 \C\C 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 \D\D endowed with the Skorohod topology.

Keywords

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

R2 v1 2026-06-22T00:34:20.117Z