Positive recurrence of a solution of an SDE with variable switching intensities

TL;DR

This paper proves positive recurrence for a multidimensional switching diffusion process with variable intensities, using embedded Markov chains, under certain conditions, contributing to the understanding of stochastic differential equations with regime switching.

Contribution

It introduces conditions for positive recurrence of switching diffusions with variable intensities, employing embedded Markov chain techniques, which advances the analysis of such stochastic systems.

Findings

Established positive recurrence under specific conditions.

Utilized embedded Markov chains for analysis.

Addressed systems with both recurrent and transient regimes.

Abstract

Positive recurrence of a $d$-dimensional diffusion with switching and with one recurrent and one transient regimes and variable switching intensities is established under suitable conditions. The approach is based on embedded Markov chains.