2021/09/12 by Claude Godrèche, J. M. Luck, Jean-Marc Luck · 6 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Acceleration #Brownian excursion #Brownian motion #Computer science #Diffusion and Search Dynamics #Diffusion process #Geometric Brownian motion #Hitting time #Limit (mathematics) #Markov process #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Random walk #Renewal theory #Statistical physics #Statistics #Stochastic process #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math.PR
paper · pdf · doi:10.1007/s10955-021-02852-9
published in Journal of Statistical Physics 186(1) (Springer Science+Business Media) · 32 pages, 7 figures
arxiv created 2021/09/12 · openalex created_date 2021/09/27 · openalex publication_date 2021/12/03 · arxiv updated 2022/03/03 · openalex updated_date 2026/08/05
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this limit, the renewal structure of the record process is the cornerstone for the analysis of its statistics. We thus obtain the analytical expressions of several characteristics of the process, notably the distribution of the total duration of record runs (sequences of consecutive records), which is the continuum analogue of the number of records of the integrated random walks. This result is universal, i.e., independent of the details of the parent distribution of the step lengths.