Joint densities for random walks in the plane

George H. Weiss; Uri Shmueli

doi:10.1016/0378-4371(87)90289-5

Joint densities for random walks in the plane

George H. Weiss^*
, Uri Shmueli

^*Corresponding author for this work

School of Chemistry

National Institutes of Health

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

4 Scopus citations

Abstract

We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for p_n(r, θ) is developed for this purpose which does not require radial symmetry, but does require that p_n(r, θ) = 0 when r exceeds some maximum radius, R.

Original language	English
Pages (from-to)	641-649
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	146
Issue number	3
DOIs	https://doi.org/10.1016/0378-4371(87)90289-5
State	Published - Dec 1987

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title = "Joint densities for random walks in the plane",

abstract = "We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for pn(r, θ) is developed for this purpose which does not require radial symmetry, but does require that pn(r, θ) = 0 when r exceeds some maximum radius, R.",

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AB - We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for pn(r, θ) is developed for this purpose which does not require radial symmetry, but does require that pn(r, θ) = 0 when r exceeds some maximum radius, R.

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Joint densities for random walks in the plane

Abstract

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