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arXiv · 1812.06409

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

Ying Chao·Jinqiao Duan
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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.

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Ying Chao, Jinqiao Duan. 2018-12-16. The Onsager-Machlup Function as Lagrangian for the Most Probable Path of a Jump-diffusion Process. https://doi.org/10.1088/1361-6544/ab248b

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