On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal–reward process

Rovshan Aliyev and Veli Bayramov

Statistics & Probability Letters, 2017, vol. 127, issue C, 138-149

Abstract: In this study, a renewal–reward process with multivariate rewards is investigated and an asymptotic expansion for the covariance function of the rewards is derived. The remainder term of the result in Patch et al. (2015) is sharpened from the o(1) to o(t−k). Moreover, asymptotic expansions as t→∞ with the remainder term o(t−k) for the mathematical expectation and variance of the renewal–reward process also are obtained.

Keywords: Renewal process; Renewal function; Renewal–reward process; Second-order approximation; Multivariate rewards (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2017.04.011

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