On the behaviour of a long cascade of linear reservoirs

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We s how that the storage in the nth reservoir becomes asymptotically determinis tic as n --> infinity, and establish a central limit theorem for the random fluctuations about the deterministic approximation. in addition, we prove a large deviations theorem that provides precise logarithmic asymptotics fo r the tail probabilities associated with the storage in the nth reservoir w hen n is large.