Action functionals for stochastic differential equations with Lévy noise

2019/08/26 by Yuan, Shenglan, Duan, Jinqiao · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.09687

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

Cited by

• Lévy noise drives an exponential acceleration in transition rates within metastable systems

Related

• Onsager-Machlup action functional for stochastic partial differential equations with Levy noise
• Large deviations for stochastic PDE with Levy noise
• Long-time behaviors of some stochastic differential equations driven by Lévy noise
• Large deviations for stochastic differential delay equations with Lévy noises
• Large deviation principles for stochastic dynamical systems with a fractional Brownian noise