Splitting and survival probabilities in stochastic random walk methods and applications

Sabelfeld Karl K. ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2016, vol. 22, issue 1, 55-72

Abstract: We suggest a series of extremely fast stochastic algorithms based on exact representations we derive in this paper for the first passage time and exit point probability densities, splitting and survival probabilities. We apply the developed algorithms to the following three classes of problems: (1) simulation of epitaxial nanowire growth, (2) diffusion imaging of microstructures, in particular, cathodoluminescence imaging for threading dislocations, and (3) simulation of the annihilation of electrons and holes in vicinity of nonradiative centers and quantum efficiency evaluation. In the last example the Random Walk on Spheres method is used to solve nonlinear diffusion equations, and to more general systems of nonlinear Smoluchowski equations combined with the kinetic Monte Carlo method.

Keywords: Survival probability; splitting probability; first passage time; cathodoluminescence; quantum efficiency (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/mcma-2016-0103

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