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Turkish Journal of Mathematics

Author ORCID Identifier

BÜŞRA ALAKOÇ: 0000-0001-8975-5968

ASLI BEKTAŞ KAMIŞLIK: 0000-0002-9776-2145

TÜLAY YAZIR: 0000-0002-8807-5677

TAHİR KHANIYEV: 0000-0003-1974-0140

DOI

10.55730/1300-0098.3559

Abstract

This study proposed moment-based approximations for the expected value and variance of the ergodic distribution of the semi-Markovian random walk process (X(t)) with gamma distributed interference of chance. Many studies have investigated analogous moment problems by using asymptotic approach. The key distinguishing aspect of this study from others in the literature is obtaining Kambo’s approximations for the moments of X(t) instead of asymptotic expansions. Firstly, the approximation formulas for the moments of boundary functional SN(z) of X(t) were obtained. Then using these results, approximation formulas for the first two moments of the ergodic distributions of X(t) were derived. Finally, the expected value and variance of X(t) were calculated by using the Monte Carlo simulation method for two concrete distributions (Gaussian and Uniform).

Keywords

Semi-Markovian random walk process, moment-based approximation, ergodic distribution, boundary functional, interference of chance.

First Page

1037

Last Page

1054

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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