2017/04/30 by Claude Godrèche
Mathematics · Physics and Astronomy · #Brownian bridge #Brownian motion #Context (archaeology) #Event (particle physics) #Expression (computer science) #First-hitting-time model #Laplace transform #Renewal theory #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Zero (linguistics) #cond-mat.stat-mech #math.PR #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/aa79b1
published as J. Stat. Mech. 073205 (2017) · 19 pages, 5 figures
openalex created_date 2017/04/28 · arxiv created 2017/06/28 · openalex publication_date 2017/07/01 · arxiv updated 2018/02/27 · openalex updated_date 2026/08/05
Abstract Tied-down renewal processes are generalisations of the Brownian bridge, where an event (or a zero crossing) occurs both at the origin of time and at the final observation time t . We give an analytical derivation of the two-time correlation function for such processes in the Laplace space of all temporal variables. This yields the exact asymptotic expression of the correlation in the Porod regime of short separations between the two times and in the persistence regime of large separations. We also investigate other quantities, such as the backward and forward recurrence times, as well as the occupation time of the process. The latter has a broad distribution which is determined exactly. Physical implications of these results for the Poland Scheraga and related models are given. These results also give exact answers to questions posed in the past in the context of stochastically evolving surfaces.