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

2020/11/19 by Jianyu Hu, Hu, Jianyu, Jinqiao Duan +1
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.2011.09690

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.

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