Existence of geometric ergodic periodic measures of stochastic differential equations

Feng, Chunrong; Zhao, Huaizhong; Zhong, Johnny

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
• Electronic ISSN: 1090-2732
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 359
• Pages: 67-106
• DOI: https://doi.org/10.1016/j.jde.2023.02.022
• Public URL: https://durham-repository.worktribe.com/output/1178430