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 L\'evy processes with existing finite exponential moments. Based on extended contraction principle, Legendre transform and L\'evy symbols, we derive the action functionals for stochastic differential equations driven by L\'evy processes.