LYAPUNOV EXPONENTS FOR NONLINEAR-SYSTEMS WITH POISSON WHITE-NOISE

The stability analysis of the solution of stochastic differential equa tions based on Lyapunov exponents is a topic of active research in app lied mathematics, physics, chemistry, and many other engineering field s. The analysis identifies subsets in the space of the parameters of a stochastic differential equation for which the solution of this equat ion remains bounded in some sense as time increases indefinitely. Howe ver, Lyapunov exponents have been calculated only for the solutions of stochastic differential equations driven by Gaussian white noise. Thi s 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 forma l derivative of the compound Poisson process. The analysis is based on a generalized version of the classical Ito differentiation formula.