Absorption of a Randomly Accelerated Particle: Gambler's Ruin in a Different Game

Abstract

We consider a particle which is randomly accelerated by Gaussian white noise on the line 0<x<1, with absorbing boundaries at x=0,1. Denoting the initial position and velocity of the particle by x_0 and v_0 and solving a Fokker-Planck type equation, we derive the exact probabilities q_0(x_0,v_0), q_1(x_0,v_0) of absorption at x=0,1, respectively. The results are in excellent agreement with computer simulations.

11 pages, 1 eps figure

References in corpus (1)

• Inelastic collapse of a randomly forced particle

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