R. Aliyev, V. Bayramov, “On asymptotic expansion for mathematical expectation of a renewal–reward process with dependent components and heavy-tailed interarrival times”, Teor. Veroyatnost. i Primenen., 2022, Volume 67, Issue 4,Pages <nobr>810

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Short Communications

On asymptotic expansion for mathematical expectation of a renewal–reward process with dependent components and heavy-tailed interarrival times

R. Aliyev^a, V. Bayramov^b

^a Department of Operations Research and Probability Theory, Baku State University, Baku, Azerbaijan
^b Institute of Control Systems, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Abstract: A renewal–reward process with dependent components and heavy-tailed interarrival times is investigated, and an asymptotic expansion as $t\to\infty$ for the expectation is derived.

Keywords: renewal process, renewal function, renewal–reward process, heavy-tailed distribution, subexponential distribution.

Received: 14.06.2021
Revised: 26.04.2022

DOI: 10.4213/tvp5223