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Variable-step-length algorithms for a random walk: Hitting probability and computation performance
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DOI：10.1016/j.cpc.2019.04.001.png)
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Abstract
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We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in case where the random walk terminates at some boundary. We recently found that a finite step of the random walk produces a bias in the hitting probability and this bias vanishes in the limit of an infinitesimal step. Therefore, it is important to know how a change in the step size of the random walk influences the performance of simulations. We propose an algorithm with the most effective procedure for the step-length-change protocol. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Random walk
Monte Carlo
Hitting probability
Laplace equation
Finite step
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