Sums and weighted sums of a gamma Markov sequence

Abstract

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

A new look at the Moran dam

“…The Moran dam has been taken as a starting point for various extensions, for example to continuous-time models with general release rules. For the generalization to Markovian input sequences see Phatarfod (1982Phatarfod ( ), (1988, Lloyd and Saleem (1979), Lloyd and Warren (1982) and the references given in these papers.…”