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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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  • Sabelfeld, Karl K.

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.

Suggested Citation

  • Sabelfeld, Karl K., 2018. "Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 137-142.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:137-142
    DOI: 10.1016/j.spl.2018.03.002
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