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Title: Approximation results for the moments of random walk with normally distributed interference of chance
Authors: Hanalıoğlu, Zülfiye
Poladova, Aynura
Khaniyev, Tahir
Keywords: Random walk
discrete interference of chance
ergodic distribution
approximation formulas
normal distribution
Weak-Convergence Theorem
Renewal-Reward Process
Gaussian Distribution
Ergodic Distribution
Issue Date: 2023
Publisher: Scientific And Technological Research Council Turkey
Abstract: In this study, a random walk process (X (t)) with normally distributed interference of chance is considered. In the literature, this process has been shown to be ergodic and the limit form of the ergodic distribution has been found. Here, unlike previous studies, the moments of the X (t) process are investigated. Although studies investigating the moment problem for various stochastic processes (such as renewal-reward processes) exist in the literature, it has not been considered for random walk processes, as it requires the use of new mathematical tools. Therefore, in this study, firstly, the exact formulas for the first four moments of the ergodic distribution of the X (t) process, which is a modification of the random walk process, are found. Due to the extremely complex mathematical structure of the exact formulas, in the second part of the study, three-term asymptotic expansions are attained for these moments. Based on the asymptotic expansions, simple and useful approximation formulas, for the moments of the process X (t) are proposed. In order to show that the approximate formulas are close enough to the exact formulas, a special example is given at the end of the study and the accuracy of the approximate formulas is examined on this example.
ISSN: 1300-0098
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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