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.