Recurrence and Ergodicity of Switching Diffusions with Past-Dependent Switching Having A Countable State Space

2017/06/26 by Dang H. Nguyen, Nguyen, Dang H., George Yin +1
Economics, Econometrics and Finance · Engineering · Mathematics · #37A50 #60H10 #60J60 #60J75 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1706.08352

openalex publication_date 2017/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time depend on the value of the continuous component over an interval including certain past history. Sufficient conditions for recurrence and ergodicity are given. Moreover, the relationship between systems of partial differential equations and recurrence when the switching is past-independent is established under suitable conditions.

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