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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. / Sabelfeld, Karl K.

In: Statistics and Probability Letters, Vol. 138, 01.07.2018, p. 137-142.

Research output: Contribution to journal › Article › peer-review

Harvard

Sabelfeld, KK 2018, 'Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations', Statistics and Probability Letters, vol. 138, pp. 137-142. https://doi.org/10.1016/j.spl.2018.03.002

APA

Sabelfeld, K. K. (2018). Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations. Statistics and Probability Letters, 138, 137-142. https://doi.org/10.1016/j.spl.2018.03.002

Vancouver

Sabelfeld KK. Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations. Statistics and Probability Letters. 2018 Jul 1;138:137-142. doi: 10.1016/j.spl.2018.03.002

Author

Sabelfeld, Karl K. / Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations. In: Statistics and Probability Letters. 2018 ; Vol. 138. pp. 137-142.

BibTeX

@article{b864c6313f60420aadf0380f9a579414,
title = "Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations",
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 = "Cathodoluminescence, Diffusion–advection equation, Random walk on spheres, Survival probability, von Mises–Fisher distribution, Diffusion advection equation, von Mises Fisher distribution",
author = "Sabelfeld, {Karl K.}",
year = "2018",
month = jul,
day = "1",
doi = "10.1016/j.spl.2018.03.002",
language = "English",
volume = "138",
pages = "137--142",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier Science B.V.",

}

RIS

TY - JOUR

T1 - Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations

AU - Sabelfeld, Karl K.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - Cathodoluminescence

KW - Diffusion–advection equation

KW - Random walk on spheres

KW - Survival probability

KW - von Mises–Fisher distribution

KW - Diffusion advection equation

KW - von Mises Fisher distribution

UR - http://www.scopus.com/inward/record.url?scp=85044446092&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2018.03.002

DO - 10.1016/j.spl.2018.03.002

M3 - Article

AN - SCOPUS:85044446092

VL - 138

SP - 137

EP - 142

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -

ID: 12214684