A Compound Poisson Dam with Exponentially Distributed Inputs and Release Rule Proportional to its Wiener Process Content

摘要

This paper focuses on the determination of the mean and the stationary distribution for a compound Poisson dam process with exponentially distributed inputs subject to release rule proportional to its content and a content forming a wiener process. The stationary distribution is obtained for finite and infinite dams. The mean and the variance of the stationary distributions are also considered. This process is originated from problems of storage of water in dams or reservoirs.