## 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 language | English |
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Pages (from-to) | 137-142 |

Number of pages | 6 |

Journal | Statistics and Probability Letters |

Volume | 138 |

DOIs | |

Publication status | Published - 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