Onsager-Machlup action functional for stochastic partial differential equations with Levy noise

TL;DR

This paper derives the Onsager-Machlup action functional for stochastic partial differential equations driven by Levy noise and Gaussian Brownian motion, facilitating the analysis of most probable transition paths in infinite-dimensional systems.

Contribution

It introduces a method to derive the Onsager-Machlup functional for SPDEs with Levy and Gaussian noise using Girsanov transformation and path representation, advancing the understanding of transition dynamics.

Findings

Derived the Onsager-Machlup functional for Levy-driven SPDEs.

Enabled analysis of most probable transition paths in infinite dimensions.

Provided a framework for studying stochastic dynamical systems with non-Gaussian noise.

Abstract

This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian motion. This is achieved by applying the Girsanov transformation for probability measures and then by a path representation. This enables the investigation of the most probable transition path for infinite dimensional stochastic dynamical systems modeled by stochastic partial differential equations, by minimizing the Onsager-Machlup action functional.