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Some ratio identities for a class of skip free random walks

Published online by Cambridge University Press:  14 July 2016

P. A. Pegg
P. A. Pegg*
Affiliation:
University of Sheffield
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Abstract

We prove a ratio identity giving a transform of the distribution of the position of a two barrier random walk as a ratio of the equivalent transforms for the one barrier random walk. This ratio identity holds for skip free random walks where the increments are dependent on both the previous increment and also the position of the random walk.

Keywords

RATIO IDENTITYSKIP FREEABSORBING BARRIERSIMPENETRABLE BARRIERSDUALITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 213 - 217
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Gani, J. (1969) Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 90–110.CrossRefGoogle Scholar
[2] Phatarfod, R. M., Speed, T. P. and Walker, A. M. (1971) A note on random walks. J. Appl. Prob. 8, 198–202.Google Scholar
[3] Prabhu, N. U. Queues and Inventories. Wiley, New York.Google Scholar
[4] Roes, P. B. M. (1970) The finite dam. J. Appl. Prob. 7, 316–326.CrossRefGoogle Scholar
[5] Speed, T. P. A note on random walks, II. J. Appl. Prob. 10, 218–222.Google Scholar
[6] Takács, L. Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar