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Volume 39, Issue 3
Recent Results on Recurrent Solutions and Limit Distributions of SDEs

Zhenxin Liu

DOI: 10.4208/cmr.2022-0036

Commun. Math. Res., 39 (2023), pp. 476-500.

Published online: 2023-04

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  • Abstract

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.

  • Keywords

Recurrent solution, stochastic differential equation, invariant measure, Markov process.

  • AMS Subject Headings

37B20, 60H10, 60J25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-476, author = {Liu , Zhenxin}, title = {Recent Results on Recurrent Solutions and Limit Distributions of SDEs}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {3}, pages = {476--500}, abstract = {

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0036}, url = {http://global-sci.org/intro/article_detail/cmr/21611.html} }
TY - JOUR T1 - Recent Results on Recurrent Solutions and Limit Distributions of SDEs AU - Liu , Zhenxin JO - Communications in Mathematical Research VL - 3 SP - 476 EP - 500 PY - 2023 DA - 2023/04 SN - 39 DO - http://doi.org/10.4208/cmr.2022-0036 UR - https://global-sci.org/intro/article_detail/cmr/21611.html KW - Recurrent solution, stochastic differential equation, invariant measure, Markov process. AB -

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.

Zhenxin Liu. (2023). Recent Results on Recurrent Solutions and Limit Distributions of SDEs. Communications in Mathematical Research . 39 (3). 476-500. doi:10.4208/cmr.2022-0036
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