The Onsager-Machlup Function as Lagrangian for the Most Probable Path of a Jump-diffusion Process

Abstract

This work is devoted to deriving the Onsager-Machlup function for a class of stochastic dynamical systems under (non-Gaussian) Levy noise as well as (Gaussian) Brownian noise, and examining the corresponding most probable paths. This Onsager-Machlup function is the Lagrangian giving the most probable path connecting metastable states for jump-diffusion processes. This is done by applying the Girsanov transformation for measures induced by jump-diffusion processes. Moreover, we have found this Lagrangian function is consistent with the result in the special case of diffusion processes. Finally, we apply this new Onsager-Machlup function to investigate dynamical behaviors analytically and numerically in several examples. These include the transitions from one metastable state to another metastable state in a double-well system, with numerical experiments illustrating most probable transition paths for various noise parameters.

arXiv comment27 pages,12 figures

References in corpus (6)

• Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle
• Convergence analysis of a finite element approximation of minimum action methods
• Stochastic analysis in a tubular neighborhood or Onsager-Machlup functions revisited
• Jump Type Stochastic Differential Equations with Non-Lipschitz Coefficients: Non Confluence, Feller and Strong Feller Properties, and Exponential Ergodicity
• What is the correct cost functional for variational data assimilation?
• The Onsager--Machlup functional for data assimilation

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