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2 results

Dams with additive inputs revisited
P. A. Pegg, R. M. Phatarfod
Journal:

Journal of Applied Probability / Volume 14 / Issue 2 / June 1977

Published online by Cambridge University Press:

14 July 2016, pp. 367-374

Print publication:

June 1977
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In this paper we consider a finite dam with unit release. Ratio identities are derived for the various random walks involved, and from them are derived the p.g.f. of the time of first emptiness with and without overflow and the complete time-dependent distribution of the dam content.

Some ratio identities for a class of skip free random walks
P. A. Pegg
Journal:

Journal of Applied Probability / Volume 10 / Issue 1 / March 1973

Published online by Cambridge University Press:

14 July 2016, pp. 213-217

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March 1973
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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.

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2 results

Dams with additive inputs revisited

Some ratio identities for a class of skip free random walks