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Existence of geometric ergodic periodic measures of stochastic differential equations

Feng, Chunrong; Zhao, Huaizhong; Zhong, Johnny

Existence of geometric ergodic periodic measures of stochastic differential equations Thumbnail


Authors

Johnny Zhong



Abstract

Periodic measures are the time-periodic counterpart to invariant measures for dynamical systems and can be used to characterise the long-term periodic behaviour of stochastic systems. This paper gives sufficient conditions for the existence, uniqueness and geometric convergence of a periodic measure for time-periodic Markovian processes on a locally compact metric space in great generality. In particular, we apply these results in the context of time-periodic weakly dissipative stochastic differential equations, gradient stochastic differential equations as well as Langevin equations. We will establish the Fokker-Planck equation that the density of the periodic measure sufficiently and necessarily satisfies. Applications to physical problems shall be discussed with specific examples.

Citation

Feng, C., Zhao, H., & Zhong, J. (2023). Existence of geometric ergodic periodic measures of stochastic differential equations. Journal of Differential Equations, 359, 67-106. https://doi.org/10.1016/j.jde.2023.02.022

Journal Article Type Article
Acceptance Date Feb 7, 2023
Online Publication Date Feb 24, 2023
Publication Date Jun 25, 2023
Deposit Date Feb 27, 2023
Publicly Available Date Feb 27, 2023
Journal Journal of Differential Equations
Print ISSN 0022-0396
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 359
Pages 67-106
DOI https://doi.org/10.1016/j.jde.2023.02.022

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