Transition Path Theory For Lévy-Type Processes: SDE Representation and Statistics

2025/06/11 by Huang, Yuanfei, Zhou, Xiang
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.09462

Abstract

This paper establishes a Transition Path Theory (TPT) for Lévy-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.

Citations

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Related

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• Reactive trajectories and the transition path process
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• Asymptotic expansion for the transition densities of stochastic differential equations driven by the gamma processes