A theory of dams with continuous input and a general release rule
- 1 April 1969
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 6 (1) , 88-98
- https://doi.org/10.2307/3212278
Abstract
Consider an infinite capacity dam in which the input and release occur continuously in time. Write X(t) for the total input up to time t starting from X(0) = 0 at t = 0. Let Z(t) be the content of the dam at time t and R(u) (0 ≦ u < ∞) a release function such that in any interval of time (t, t + dt), the amount of water released is R(Z(t))dt + o(t) for any bounded realisation of the process {Z(t)}. Thus R(u) can be regarded as a “rate of release”.Keywords
This publication has 3 references indexed in Scilit:
- Dams in series with continuous releaseJournal of Applied Probability, 1967
- A storage model with continuous infinitely divisible inputsMathematical Proceedings of the Cambridge Philosophical Society, 1963
- A PROBABILITY THEORY OF A DAM WITH A CONTINUOUS RELEASEThe Quarterly Journal of Mathematics, 1956