On dams with additive inputs and a general release rule

Abstract

An infinite capacity dam subject to an additive input process and a general release rule is considered. The input process can have infinitely many jumps in any finite interval, and the rate of release is r(x) when the dam content is x. The content is constructed as the increasing limit of a sequence of Markov processes and the convergence is shown to be almost surely uniform over finite intervals. The limit process is shown to be a standard Markov process and its characteristic equation is computed.