Lyapunov exponents for nonlinear systems with Poisson white noise

Abstract

The stability analysis of the solution of stochastic differential equations based on Lyapunov exponents is a topic of active research in applied mathematics, physics, chemistry, and many other engineering fields. The analysis identifies subsets in the space of the parameters of a stochastic differential equation for which the solution of this equation remains bounded in some sense as time increases indefinitely. However, Lyapunov exponents have been calculated only for the solutions of stochastic differential equations driven by Gaussian white noise. This is a significant limitation because many stochastic disturbances are not Gaussian. This paper calculates Lyapunov exponents for stochastic differential equations with Poisson white noise, defined as the formal derivative of the compound Poisson process. The analysis is based on a generalized version of the classical Itô differentiation formula.