Stochastic stability of dynamical systems driven by Lévy processes

This paper examines the asymptotic stability of dynamical systems that are driven by Lévy processes. A Lévy process is a stochastic process with stationary and independent increments. It includes both Wiener and Poisson jump processes and is suitable for simultaneous modeling of small and large fluctuations in a system. Sufficient conditions for the asymptotic stability of the process´ sample paths are derived based on Lyapunov-like techniques. In particular, both the linear and nonlinear models of the process are investigated in the presented stability analyses.