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We apply the developed algorithms to the following three classes of problems: (1) simulation\nof 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,\nand to more general systems of nonlinear Smoluchowski equations combined with the kinetic Monte Carlo method.<\/jats:p>","DOI":"10.1515\/mcma-2016-0103","type":"journal-article","created":{"date-parts":[[2016,3,2]],"date-time":"2016-03-02T08:25:12Z","timestamp":1456907112000},"page":"55-72","source":"Crossref","is-referenced-by-count":12,"title":["Splitting and survival probabilities in stochastic random walk methods and applications"],"prefix":"10.1515","volume":"22","author":[{"given":"Karl K.","family":"Sabelfeld","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,3,2]]},"reference":[{"key":"2023040101023276169_j_mcma-2016-0103_ref_000_w2aab2b8b8b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"S. 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