2010/01/31 by Satya N. Majumdar, Satya N Majumdar, Alberto Rosso +1 · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Acceleration #Advanced Thermodynamics and Statistical Mechanics #Boundary (topology) #Brownian bridge #Brownian motion #Hitting time #Interval (graph theory) #Process (computing) #Stochastic process #Stochastic processes and financial applications #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/43/11/115001
published as J. Phys. A: Math. Theor. 43, 115001 (2010) · 17 pages, 5 figures Typo in Eq. (B.11) corrected
openalex publication_date 2010/03/02 · openalex created_date 2016/06/24 · arxiv created 2019/09/01 · arxiv updated 2019/09/04 · openalex updated_date 2026/08/05
We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the probability density p ( t m | T ) of the time t m at which the process reaches its maximum, within a fixed time interval [0, T ]. We study two different boundary conditions, which correspond to the process representing respectively (i) the integral of a Brownian bridge and (ii) the integral of a free Brownian motion. Our analytical results are also verified by numerical simulations.