# Almost Sure and Moment Exponential Stability of Regime-Switching Jump Diffusions

## TL;DR

This paper investigates the stability of regime-switching jump diffusions using Lyapunov functions, providing new conditions for both nonlinear and linear systems, including necessary and sufficient criteria for one-dimensional linear cases.

## Contribution

It introduces new stability conditions for regime-switching jump diffusions, with explicit criteria for linear systems and illustrative examples.

## Key findings

- Derived sufficient stability conditions for nonlinear systems
- Established necessary and sufficient conditions for linear systems
- Provided examples demonstrating the application of the results

## Abstract

This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further helps to derive easily verifiable conditions for linear systems. For one-dimensional linear regime-switching jump diffusions, necessary and sufficient conditions for almost sure and $p$th moment exponential stabilities are presented. Several examples are provided for illustration.