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Invariant imbedding and dams with Markovian input rate
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- Journal:
- Journal of Applied Probability / Volume 17 / Issue 3 / September 1980
- Published online by Cambridge University Press:
- 14 July 2016, pp. 778-789
- Print publication:
- September 1980
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- Article
- Export citation
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The method of invariant imbedding, used extensively in astrophysics and in neutron transport theory, is applied to the analysis of dams whose input rate is a finite state-space continuous-parameter Markov chain. Passage-time distributions are considered as functions of the dam capacity. When the release rate is constant the method yields first-order non-linear differential equations with initial conditions obtained from the easily derived behaviour of a dam with zero capacity. Solutions of these equations are given. Some possible correlation functions for the increments of the cumulative input process are examined when the underlying Markov chain is stationary. Finally the analysis is extended to deal with dams having content-dependent release-rate of the form
