On entrance times of a homogeneous N-dimensional random walk: an identity
- 1 January 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (A) , 321-333
- https://doi.org/10.2307/3214166
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
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