First Passage of a Randomly Accelerated Particle · arXivDesk
1603.07017Mar 22, 201626 pages, 2 figures, Chapter 2 in First-Passage Phenomena and Their Applications, edited by R. Metzler, G. Oshanin, and S. Redner (World Scientific, 2014)
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
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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<x<1
. Then the close connection between the extreme value statistics of a randomly accelerated particle and its first-passage properties is discussed. Finally some applications where first-passage statistics of the random acceleration process play a role are considered.