Approximation results for the moments of random walk with normally distributed interference of chance

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dc.contributor.authorHanalioglu, Zulfiye
dc.contributor.authorPoladova, Aynura
dc.contributor.authorKhaniyev, Tahir
dc.date.accessioned2024-09-29T16:09:55Z
dc.date.available2024-09-29T16:09:55Z
dc.date.issued2023
dc.departmentKarabük Üniversitesien_US
dc.description.abstractIn 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.en_US
dc.identifier.doi10.55730/1300-0098.3363
dc.identifier.endpage350en_US
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85147701373en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage333en_US
dc.identifier.trdizinid1160058en_US
dc.identifier.urihttps://doi.org/10.55730/1300-0098.3363
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/1160058
dc.identifier.urihttps://hdl.handle.net/20.500.14619/7837
dc.identifier.volume47en_US
dc.identifier.wosWOS:000923127700021en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakTR-Dizinen_US
dc.language.isoenen_US
dc.publisherTubitak Scientific & Technological Research Council Turkeyen_US
dc.relation.ispartofTurkish Journal of Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectRandom walken_US
dc.subjectdiscrete interference of chanceen_US
dc.subjectergodic distributionen_US
dc.subjectapproximation formulasen_US
dc.subjectnormal distributionen_US
dc.titleApproximation results for the moments of random walk with normally distributed interference of chanceen_US
dc.typeArticleen_US

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