Existence of Geometric Ergodic Periodic Measures of Stochastic Differential Equations

Chunrong Feng; Huaizhong Zhao; Johnny Zhong

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arXiv · 1904.08091

Existence of Geometric Ergodic Periodic Measures of Stochastic Differential Equations

Chunrong Feng·Huaizhong Zhao·Johnny Zhong

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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.

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BibTeX RIS

Chunrong Feng, Huaizhong Zhao, Johnny Zhong. 2019-04-17. Existence of Geometric Ergodic Periodic Measures of Stochastic Differential Equations. https://arxiv.org/abs/1904.08091

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