Existence of Geometric Ergodic Periodic Measures of Stochastic Differential Equations
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.
Keywords
Cite
@article{arxiv.1904.08091,
title = {Existence of Geometric Ergodic Periodic Measures of Stochastic Differential Equations},
author = {Chunrong Feng and Huaizhong Zhao and Johnny Zhong},
journal= {arXiv preprint arXiv:1904.08091},
year = {2019}
}