ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.

Ora E. Percus; Jerome K. Percus

doi:10.1137/0147072

ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.

Ora E. Percus, Jerome K. Percus

Mathematics

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Abstract

We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.

Original language	English (US)
Pages (from-to)	1103-1111
Number of pages	9
Journal	SIAM Journal on Applied Mathematics
Volume	47
Issue number	5
DOIs	https://doi.org/10.1137/0147072
State	Published - 1987

ASJC Scopus subject areas

Applied Mathematics

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10.1137/0147072

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title = "ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.",

abstract = "We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.",

author = "Percus, {Ora E.} and Percus, {Jerome K.}",

year = "1987",

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N2 - We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.

AB - We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.

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ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.

Abstract

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