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 x0 and v0 and solving a Fokker-Planck type equation, we derive the exact probabilities q0(x0,v0), q1(x0,v0) of absorption at x=0,1, respectively. The results are in excellent agreement with computer simulations.
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