On infinite dams with inputs forming a stationary process
- 1 September 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (03) , 553-561
- https://doi.org/10.1017/s0021900200096339
Abstract
This paper considers a dam of infinite capacity with a discrete-valued stationary input process and a unit release whenever possible. It is shown how, by suitable manipulations of the equation governing the dam content process, the stationary distribution of the dam being empty can be obtained, as also can (with a few additional assumptions) the expected value of the dam content in the stationary case. Results obtained are applied to particular cases of input — independent and identical, Markov, Bivariate Markov and moving-average.Keywords
This publication has 9 references indexed in Scilit:
- On dams with Markovian inputsJournal of Applied Probability, 1973
- Some results for dams with Markovian inputsJournal of Applied Probability, 1973
- An infinite discrete dam with dependent inputsJournal of Applied Probability, 1972
- Reservoirs with Mixed Markovian-Independent InflowsSIAM Journal on Applied Mathematics, 1972
- A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflowsJournal of Applied Probability, 1971
- A population process with Markovian progeniesJournal of Mathematical Analysis and Applications, 1970
- Infinite dams with inputs forming a Markov chainJournal of Applied Probability, 1968
- A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawalsJournal of Applied Probability, 1965
- Some Exact Results for the Finite DamThe Annals of Mathematical Statistics, 1958