Coupling and Exponential Convergence Rate for Markovian Switching Jump Diffusions

Abstract

This work is concerned with coupling and exponential convergence rate for a class of Markovian switching jump-diffusion processes. The processes under consideration can be thought of as a number of jump-diffusion processes modulated by a Markovian switching device. For this class of processes, we construct some order-preserving couplings. Furthermore, by virtue of the coupling results, we also provide an estimate of exponential convergence rate for the Markovian switching jump-diffusion processes without Gaussian noise.

Keywords:

• Jump diffusion
• Markovian switching
• Coupling
• Exponential convergence rate

2000 Mathematics Subject Classification:

• 60J25
• 60J60