Transition Path Theory For L\'{e}vy-Type Processes: SDE Representation and Statistics
Probability
2026-05-04 v2 Mathematical Physics
math.MP
Abstract
This paper establishes a Transition Path Theory (TPT) for L\'{e}vy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non-Gaussian stochastic systems. A key contribution is the rigorous derivation of the stochastic differential equation (SDE) representation for transition path processes, which share the same distributional properties as transition trajectories, along with a proof of its well-posedness. This result provides a solid theoretical foundation for sampling transition trajectories. The paper also investigates the statistical properties of transition trajectories, including their probability distribution, probability current, and rate of occurrence.
Cite
@article{arxiv.2506.09462,
title = {Transition Path Theory For L\'{e}vy-Type Processes: SDE Representation and Statistics},
author = {Yuanfei Huang and Xiang Zhou},
journal= {arXiv preprint arXiv:2506.09462},
year = {2026}
}