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

D. J. Bicout·T. W. Burkhardt
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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.

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D. J. Bicout, T. W. Burkhardt. 2000-11-15. Absorption of a Randomly Accelerated Particle: Gambler's Ruin in a Different Game. https://doi.org/10.1088/0305-4470%2F33%2F39%2F301

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