2016/03/22 by Theodore W. Burkhardt, Burkhardt, Theodore W. · 2 citations
Mathematics · Physics and Astronomy · #Acceleration #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Interval (graph theory) #Mathematical Physics (math-ph) #Mathematics #Orbital Angular Momentum in Optics #Particle (ecology) #Physics #Position (finance) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Statistics #White noise #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1603.07017
published in arXiv (Cornell University) (Cornell University) · 26 pages, 2 figures, Chapter 2 in First-Passage Phenomena and Their Applications, edited by R. Metzler, G. Oshanin, and S. Redner (World Scientific, 2014)
openalex publication_date 2016/03/22 · arxiv created 2016/03/24 · arxiv updated 2016/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
In the random acceleration process, a point particle is accelerated according to x=η(t), where the right hand side represents Gaussian white noise with zero mean. We begin with the case of a particle with initial position x0 and initial velocity v0 and review the statistics of its first arrival at the origin and its first return to the origin. Multiple returns to the origin, motion with a constant force in addition to a random force, and persistence properties for several boundary conditions at the origin are also considered. Next we review first-exit properties of a randomly accelerated particle from the finite interval 0