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Diffusion in Random Fields pp 47–89Cite as

Birkhäuser

Stochastic Simulations of Diffusion Processes

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Part of the book series: Geosystems Mathematics ((GSMA))

Abstract

Random sequences, their numerical simulation, and convergence properties are shortly introduced as basic tools in solving stochastic differential equations. Strong and weak solutions of Itô equations will be defined and illustrated for the Euler scheme. The global random walk (GRW) algorithm will be introduced as a superposition of arbitrarily large numbers of Euler schemes on regular lattices. Unbiased and biased GRW algorithms will be described and their relation to Fokker–Planck and Itô equations will be discussed.

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Authors and Affiliations

  1. Department of Mathematics, Friedrich-Alexander University of Erlangen-Nürnberg, Erlangen, Germany

    Nicolae Suciu

  2. Tiberiu Popoviciu Institute of Numerical Analysis, Cluj-Napoca Branch of the Romanian Academy, Cluj-Napoca, Romania

    Nicolae Suciu

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  1. Nicolae Suciu
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Suciu, N. (2019). Stochastic Simulations of Diffusion Processes. In: Diffusion in Random Fields . Geosystems Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-15081-5_3

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