LIMITING COVARIANCE IN MARKOV-RENEWAL PROCESSES
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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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.
- Statistics and Probability