Transition pathways for a class of degenerate stochastic dynamical systems with Lévy noise

2025/01/09 by Chao, Ying, Wei, Pingyuan
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2501.05215

Abstract

This work is devoted to deriving the Onsager--Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) Lévy noise as well as Brownian noise. This is obtained based on the Girsanov transformation and then by a path representation. Moreover, this Onsager--Machlup function may be regarded as a Lagrangian giving the most probable transition pathways. The Hamilton--Pontryagin principle is essential to handle such a variational problem in degenerate case. Finally, a kinetic Langevin system in which noise is degenerate is specifically investigated analytically and numerically.

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