2009/05/04 by Michele Maggiore, Maggiore, Michele, Antonio Riotto +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Diffusion and Search Dynamics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0905.0376
5 pages, 1 figure
arxiv created 2009/05/04 · openalex publication_date 2009/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits elegant analytic solutions derived from the Fokker-Planck equation with an absorbing boundary condition while, when the underlying dynamics is non-markovian, the equation for the probability becomes non-local due to the appearance of memory terms, and the problem becomes much harder to solve. We show that the computation of the probability distribution and of the first-passage time for non-Markovian processes can be mapped into the evaluation of a path-integral with boundaries, and we develop a technique for evaluating perturbatively this path integral, order by order in the non-Markovian terms.