Abstract

Abstract : General additive functions called rewards are defined on a 'regular' finite-state Markov-renewal process. The asymptotic form of the mean total reward in (O, t) has previously been obtained, and it is known that the total rewards are joint-normally distributed as t approaches infinity. This paper finds the dominant asymptotic term in the covariance of the total rewards as a simple function of the moments of the per-transition rewards, and the 'bias' term of the mean total rewards. Special formulas for the dominant covariance term of 'number of visits', and 'occupation time' in given states are also derived.

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