Abstract
This note deals with some aspects of transition probability matrices as used in Markov chains, with particular reference to their rôles in Stochastic Reservoir and Flood Cascade Theories. Rationalising the approach to multivariate Markov chains, it is shown that heretofore complicated problems can be dealt with in a unified manner. Sums of Markov chains are shown to be, in a sense, Markovian, which opens the door to dealing with systems of more than one reservoir. A flood cascade model is developed which allows probabilistic comparisons to be made of the flood attenuation capabilities of various dam layouts.
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