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Some explicit results for correlated random walks

Published online by Cambridge University Press:  14 July 2016

Ram Lal  and
U. Narayan Bhat
Ram Lal
Affiliation:
Southern Methodist University
U. Narayan Bhat*
Affiliation:
Southern Methodist University
*
∗ Postal address for both authors: Department of Statistical Science, Southern Methodist University, Dallas, TX 75275, USA.
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Abstract

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

Keywords

MARKOV CHAINEQUILIBRIUM SOLUTIONFIRST-PASSAGE PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 757 - 766
Copyright
Copyright © Applied Probability Trust 1989 

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