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

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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.

Original languageEnglish
Pages (from-to)137-142
Number of pages6
JournalStatistics and Probability Letters
Volume138
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • Cathodoluminescence
  • Diffusion–advection equation
  • Random walk on spheres
  • Survival probability
  • von Mises–Fisher distribution
  • Diffusion advection equation
  • von Mises Fisher distribution

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