Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations

Karl K. Sabelfeld

Statistics & Probability Letters, 2018, vol. 138, issue C, 137-142

Abstract: We suggest a new efficient and reliable random walk method, continuous both in space and time, for solving high-dimensional diffusion–advection–reaction equations. It is based on a discovered intrinsic relation between the von Mises–Fisher distribution on a sphere with this type of equations. It can be formulated as follows: the von Mises–Fisher distribution uniquely defines the solution of a diffusion–advection equation in any bounded or unbounded domain if the relevant boundary value problem for this equation satisfies regular existence and uniqueness conditions. Both two- and three-dimensional transient equations are included in our considerations. The accuracy and the cost of the suggested random walk on spheres method are estimated.

Keywords: von Mises–Fisher distribution; Diffusion–advection equation; Survival probability; Random walk on spheres; Cathodoluminescence (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.03.002

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