English

Transition pathways for a class of degenerate stochastic dynamical systems with L\'evy noise

Dynamical Systems 2025-01-10 v1 Probability

Abstract

This work is devoted to deriving the Onsager--Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) L\'{e}vy 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.

Keywords

Cite

@article{arxiv.2501.05215,
  title  = {Transition pathways for a class of degenerate stochastic dynamical systems with L\'evy noise},
  author = {Ying Chao and Pingyuan Wei},
  journal= {arXiv preprint arXiv:2501.05215},
  year   = {2025}
}