The Onsager-Machlup Action Functional For Stochastic Differential Equations Drived By G-Brownian Motion

This paper is devoted to deriving the Onsager-Machlup action functional for stochastic differential equations drived by G-Brownian motion.First,we derive the Onsager-Machlup action functional for stochastic differential equations with constant diffusion coefficients driven by G-Brownian motion.Our argument is based on the application of Girsanov Theorem for G-Brownian motion and the path integral represention.Then we also derive the Onsager-Machlup action functional for stochastic differential equations drived by a class of special geometric G-Brownian motion.Finally,with the help of OnsagerMachlup action functional we can find the most probable transition paths for stochastic differential equations drived by G-Brownian motion by minimizing the Onsager-Machlup action functional.