Action Functionals for Stochastic Differential Equations with Lévy Noise

Abstract

By using large deviation theory that deals with the decay of probabilities of rare events on an exponential scale, we study the longtime behaviors and establish action functionals for scaled Brownian motion and Levy processes with existing finite exponential moments. Based on extended contraction principle, Legendre transform and Levy symbols, we derive the action functionals for stochastic differential equations driven by Levy processes.