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On the time to first overflow in dams with inputs forming a Markov chain
Douglas P. Kennedy
Journal:

Journal of Applied Probability / Volume 15 / Issue 1 / March 1978

Published online by Cambridge University Press:

14 July 2016, pp. 171-178

Print publication:

March 1978
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A finite dam is studied in which the net input in each period, i.e. the excess of input over demand, is a function of a Markov chain. By using a martingale, the joint distribution of the time to first overflow and the cumulative unsatisfied demand until overflow is investigated. The probability of overflow before the unsatisfied demand exceeds a fixed level is also considered.

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On the time to first overflow in dams with inputs forming a Markov chain