Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-06T01:14:29.800Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition probability matrices for correlated random walks

Published online by Cambridge University Press:  14 July 2016

R. B. Nain  and
Kanwar Sen
R. B. Nain*
Affiliation:
Delhi University
Kanwar Sen*
Affiliation:
Delhi University
*
∗Postal address: Department of Mathematical Statistics, Delhi University, Delhi 110007, India.
∗Postal address: Department of Mathematical Statistics, Delhi University, Delhi 110007, India.
Get access Rights & Permissions [Opens in a new window]

Abstract

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Keywords

CORRELATED RANDOM WALKSTRANSITION PROBABILITY MATRICESELASTIC BARRIERSABSORBING BARRIERSREFLECTING BARRIERSMULTIPLE FUNCTION BARRIERS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 253 - 258
Copyright
Copyright © Applied Probability Trust 1980 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Gillis, J. (1955) Correlated random walk. Proc. Camb. Phil. Soc. 51, 639–651.Google Scholar
Jain, G. C. (1971) Some results in a correlated random walk. Canad. Math. Bull. 14,341–347.Google Scholar
Jain, G. C. (1973) On the expected number of visits of a particle before absorption in a correlated random walk. Canad. Math. Bull. 16, 389–396.Google Scholar
Mohan, C. (1955) The gambler's ruin problem with correlation. Biometrika 42, 486–493.Google Scholar
Proudfoot, A. D. and Lampard, D. G. (1972) A random walk problem with correlation. J. Appl. Prob. 9, 436–440.CrossRefGoogle Scholar
Seth, A. (1963) The correlated unrestricted random walk. J. R. Statist. Soc. B25, 394–400.Google Scholar
Spitzer, F. (1976) Principles of Random Walk, 2nd edn. Springer-Verlag, Berlin.Google Scholar