RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2024 Volume 115, Issue 6, Pages 987–997 (Mi mzm14076)

Papers published in the English version of the journal

Asymptotic Expansions for the Stationary Moments of a Modified Renewal-Reward Process with Dependent Components

A. Poladovaa, S. Tekina, T. Khaniyevab

a Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey
b The Center of Digital Economics, Azerbaijan State University of Economics, Baku, Azerbaijan

Abstract: In this paper, a modification of a renewal-reward process $X(t)$ with dependent components is mathematically constructed and the stationary characteristics of this process are studied. Stochastic processes with dependent components have rarely been studied in the literature owing to their complex mathematical structure. We partially fill the gap by studying the effect of the dependence assumption on the stationary properties of the process $X(t)$. To this end, first, we obtain explicit formulas for the ergodic distribution and the stationary moments of the process. Then we analyze the asymptotic behavior of the stationary moments of the process by using the basic results of the renewal theory and the Laplace transform method. Based on the analysis, we obtain two-term asymptotic expansions of the stationary moments. Moreover, we present two-term asymptotic expansions for the expectation, variance, and standard deviation of the process $X(t)$. Finally, the asymptotic results obtained are examined in special cases.

Keywords: renewal-reward process, regenerative process, dependent components, moments of ergodic distribution, asymptotic expansion.

MSC: 60G50, 60K15, 60K05

Received: 15.06.2023
Revised: 07.05.2024

Language: English


 English version:
Mathematical Notes, 2024, 115:6, 987–997

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024