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Splitting and survival probabilities in stochastic random walk methods and applications

Author

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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)

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.

Suggested Citation

  • Sabelfeld Karl K., 2016. "Splitting and survival probabilities in stochastic random walk methods and applications," Monte Carlo Methods and Applications, De Gruyter, vol. 22(1), pages 55-72, March.
    • Handle: RePEc:bpj:mcmeap:v:22:y:2016:i:1:p:55-72:n:4
    DOI: 10.1515/mcma-2016-0103
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    References listed on IDEAS

    as
    1. Sabelfeld K. & Mozartova N., 2009. "Sparsified Randomization Algorithms for large systems of linear equations and a new version of the Random Walk on Boundary method," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 257-284, January.
    2. Kolodko, A. & Sabelfeld, K. & Wagner, W., 1999. "A stochastic method for solving Smoluchowski's coagulation equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 57-79.
    3. Sabelfeld, Karl & Kolodko, Anastasia, 2003. "Stochastic Lagrangian models and algorithms for spatially inhomogeneous Smoluchowski equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 115-137.
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