Journal article

A correction term for the covariance of renewal-reward processes with multivariate rewards

Brendan Patch, Yoni Nazarathy, Thomas Taimre



We consider a renewal-reward process with multivariate rewards. Such a process is constructed from an i.i.d.sequence of time periods, to each of which there is associated a multivariate reward vector. The rewards in each time period may depend on each other and on the period length, but not on the other time periods. Rewards are accumulated to form a vector valued process that exhibits jumps in all coordinates simultaneously, only at renewal epochs.We derive an asymptotically exact expression for the covariance function (over time) of the rewards, which is used to refine a central limit theorem for the vector of rewards. As illustrated by a numerical example, this refinement can yield improv..

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University of Melbourne Researchers


Awarded by Australian Research Council (ARC)

Funding Acknowledgements

This work was in part carried out as a component of the M.Sc. of BP. YN was supported by Australian Research Council (ARC) grants DP130100156 and DE130100291.