Limit Behavior of a Multi-Compartment Storage Model with an Underlying Markov Chain. II. With Normalization

摘要

This paper considers a multi-compartment storage model with one way flow. The inputs and outputs for each compartment are controlled by a denumerable state Markov chain. Assuming finite first and second moment conditions, the limit behavior of the compartments are examined. It is shown that the diverging compartments under suitable normalization converge to functionals of multivariate Brownian motion, independent of those compartments which converge without normalization. (Author)