On sufficient conditions of transience for a stochastic differential equation with switching

TL;DR

This paper investigates the conditions under which a switching Markov diffusion process is transient or ergodic, highlighting limitations in existing criteria for exponential ergodicity.

Contribution

It establishes sufficient conditions for transience and discusses the limitations of current conditions for exponential ergodicity in switching systems.

Findings

Conditions for transience are established for Markov diffusion with switching.

Limitations on conditions for exponential ergodicity are demonstrated.

Insights into the behavior of switching systems under various conditions.

Abstract

Conditions sufficient for the transience of the process have been established for the Markov diffusion model with switching and two modes, transient and ergodic, with intensities bounded away from zero. This paper shows limitations on the conditions for exponential ergodicity with a given switching system.