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A random walk problem with correlation

Published online by Cambridge University Press:  14 July 2016

A. D. Proudfoot  and
D. G. Lampard
A. D. Proudfoot
Affiliation:
Monash University
D. G. Lampard
Affiliation:
Monash University
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Abstract

The higher-order transition probability generating functions for a random-walk with correlation between steps is calculated as a discrete-domain Green's function.

Keywords

CORRELATED PROCESSDISCRETE GREEN'S FUNCTIONGAMBLER'S RUINGENERATING FUNCTIONORTHOGOṅAL POLYNOMIALRANDOM WALK
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 436 - 440
Copyright
Copyright © Applied Probability Trust 1972 

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References

Karlin, S. and Macgregor, J. (1959) Random walks. Ill. J. Math. 3, 66–81.Google Scholar
Lampard, D. G. (1967) Dual orthogonality. To be published.Google Scholar
Mohan, C. (1955) The Gambler's Ruin Problem with correlation. Biometrika 42, 486–493.Google Scholar
Proudfoot, A. D. (1971) Two classes of Markov chains, part II. Report No. MEE 71–1, Electrical Engineering Department, Monash University.Google Scholar