Recurrence and Ergodicity for A Class of Regime-Switching Jump Diffusions

TL;DR

This paper investigates the long-term behavior of regime-switching jump diffusions, establishing conditions for recurrence, ergodicity, and invariant measures, thus advancing understanding of their stability and statistical properties.

Contribution

It provides new conditions for recurrence, positive recurrence, and ergodicity in regime-switching jump diffusions, including proofs of invariant measure existence.

Findings

Conditions for recurrence and positive recurrence derived

Ergodicity of the processes established

Existence of invariant probability measures proved

Abstract

This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying processes feature in the switching process depends on the jump diffusions. In this paper, conditions for recurrence and positive recurrence are derived. Ergodicity is examined in detail. Existence of invariant probability measures is proved.