Asymptotic Expansions for the Moments of the Renewal-Reward Process With a Normal Distributed Interference of Chance

Abstract

In this study, a renewal-reward process with a normal distributed interference of chance is mathematically constructed. The ergodicity of this process is discussed. The exact formulas for the nth order moments of the ergodic distribution of the process are obtained, when the interference of chance has a truncated normal distribution with parameters (a, sigma(2)). Using these results, we derive the asymptotic expansions with three terms for the nth order moments of the ergodic distribution, when a -> infinity. Finally, the accuracy of the approximation formulas for the nth order moments of the ergodic distribution are tested by the Monte Carlo simulation method.

[Hanalioglu, Z.] Karabuk Univ, Dept Actuarial Sci & Risk Management, TR-78050 Karabuk, Turkey; [Unver, N. Fescioglu; Khaniyev, T.] TOBB Univ Econ & Technol, Dept Ind Engn, TR-06560 Ankara, Turkey; [Khaniyev, T.] Azerbaijan Natl Acad Sci, Inst Control Syst, Baku, Azerbaijan