Asymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrier

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dc.authoridGEVER, BASAK/0000-0001-6414-508X
dc.contributor.authorKhaniyev, Tahir
dc.contributor.authorGever, Basak
dc.contributor.authorHanalioglu, Zulfiye
dc.date.accessioned2024-09-29T15:50:53Z
dc.date.available2024-09-29T15:50:53Z
dc.date.issued2016
dc.departmentKarabük Üniversitesien_US
dc.description3rd International Conference on Applied Mathematics and Approximation Theory (AMAT) -- MAY 18-21, 2015 -- TOBB Econ & Technol Univ, Ankara, TURKEYen_US
dc.description.abstractIn this study, a renewal-reward process (X(t)) with a generalized reflecting barrier is constructed mathematically and under some weak conditions, the ergodicity of the process is proved. The explicit form of the ergodic distribution is found and after standardization, it is shown that the ergodic distribution converges to the limit distribution R(x), when lambda -> infinity, i. e., QX (lambda x) [GRAPHICS] P{X(t) <= lambda x} -> R(x) 2/m(2) [GRAPHICS] [1 - F(u)]dudv. Here, F(x) is the distribution function of the initial random variables {eta(n)}, n = 1, 2,..., which express the amount of rewards and m(2) = E(eta(2)(1)). Finally, to evaluate asymptotic rate of the weak convergence, the following inequality is obtained: vertical bar QX (lambda x) - R(x)vertical bar <= 2/lambda vertical bar pi(0)(x) - R(x)vertical bar. Here, pi(0)(x) = (1/m(1)) [GRAPHICS] (1 - F(u))du is the limit distribution of residual waiting time generated by {eta(n)}, n = 1, 2,..., and m(1) = E(eta(1)).en_US
dc.identifier.doi10.1007/978-3-319-30322-2_22
dc.identifier.endpage331en_US
dc.identifier.isbn978-3-319-30322-2
dc.identifier.isbn978-3-319-30320-8
dc.identifier.issn2194-5357
dc.identifier.scopus2-s2.0-84961711933en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage313en_US
dc.identifier.urihttps://doi.org/10.1007/978-3-319-30322-2_22
dc.identifier.urihttps://hdl.handle.net/20.500.14619/3782
dc.identifier.volume441en_US
dc.identifier.wosWOS:000377864300022en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer-Verlag Berlinen_US
dc.relation.ispartofIntelligent Mathematics Ii: Applied Mathematics and Approximation Theoryen_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectMarkovian Random-Walken_US
dc.subjectModelen_US
dc.subjectS,Sen_US
dc.titleAsymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrieren_US
dc.typeConference Objecten_US

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