On continuous time models in the theory of dams

Author:

Kingman J. F. C.

Abstract

The problem of storage in an infinite dam with a continuous release has been studied by a number of authors ([5], [3], [2]), who have formulated it in probabilistic terms by supposing the input to be a continuous time stochastic process. These authors have encountered difficulties which they have overcome by regarding the continuous time problem as a limit of discrete time analogues. analogues. The purpose of this paper is to suggest that these difficulties are the result of an unfortunate specification of the problem, and to show that the adoption of a slightly different (and more realistic) formulation avoids the difficulties and allows a treatment which does not have recourse to discrete time analogues.

Publisher

Cambridge University Press (CUP)

Reference6 articles.

1. Some Combinatorial Theorems for Continuous Parameter Processes.

2. The content of a dam as the supremum of an infinitely divisible process;Gani;J. Math. Mech.,1960

3. A storage model with continuous infinitely divisible inputs

4. Combinatory methods and stochastic Kolmogorov equations in the theory of queues with one server;Beneš;Trans. Amer. Math. Soc.,1960

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