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On entrance times of a homogeneous N-dimensional random walk: an identity

Published online by Cambridge University Press:  14 July 2016

J. W. Cohen
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Abstract

Present developments in computer performance evaluation require detailed analysis of N-dimensional random walks on the set of lattice points in the first 2N-ant of Recent research has shown that for the two-dimensional case the inherent mathematical problem can often be formulated as a boundary value problem of the Riemann–Hilbert type. The paper is concerned with a derivation and analysis of an identity for the first entrance times distributions into the boundary of such random walks. The identity formulates a relation between these distributions and the zero-tuples of the kernel of the random walk; the kernel contains all the information concerning the structure of the random walk in the interior of its stage space. For the two-dimensional case the identity is resolved and explicit expressions for the entrance times distributions are obtained.

Keywords

KERNELZERO-TUPLESBOUNDARY VALUE PROBLEMIDENTITY FOR ENTRANCE TIMESTABOO PROBABILITIESRIEMANN BOUNDARY VALUE PROBLEM
Type
Part 8 - Random Walks, Graphs and Networks
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 321 - 333
Copyright
Copyright © Applied Probability Trust 1988 

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References

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