Intuitive approximations for the renewal function

Mitov, Kosto V.; Omey, Edward

doi:10.1016/j.spl.2013.09.030

Cited by 13 publications

(16 citation statements)

References 10 publications

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“…Mitov and Omey [18] investigated some asymptotic properties of the class of Γ(g) . When tail distribution belongs to the extended class of Γ(g) , i.e.F (x) = P {η 1 > x} ∈ Γ(g) they also provided intuitive approximation for the renewal function generated by the random variables {η n } n≥1 as follows:…”

Section: Definition 11 a Positive And Measurable Function H Belongs To The Class Of γ(G) With Auxiliary Function G If And Only If Every Fmentioning

confidence: 99%

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A semi-Markovian renewal reward process withΓ(g)distributed demand

Kamişlik¹,

Alakoç²,

Kesemen³

et al. 2020

Turk J Math

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We consider a classical semi-Markovian stochastic model of type (s, S) with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as Γ(g) that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process X(t) which represents semi-Markovian renewal reward process of type (s, S) .We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for n th order moments of ergodic distribution of the process X(t) .

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Section: Definition 11 a Positive And Measurable Function H Belongs To The Class Of γ(G) With Auxiliary Function G If And Only If Every Fmentioning

confidence: 99%

“…Geluk [11] took the results of Anderson and Athreya [5] one step further and obtained asymptotic expansion for renewal function generated by regularly varying random variables with infinite variance. For more recent work we refer the interested reader to [9][10][11]18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A semi-Markovian renewal reward process withΓ(g)distributed demand

Kamişlik¹,

Alakoç²,

Kesemen³

et al. 2020

Turk J Math

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“…More recently [13] introduced a new method to obtain approximations for univariate renewal functions and these approximations cover the known results. In this paper we generalize these approximations to bivariate renewal processes.…”

Section: Introductionmentioning

confidence: 97%

Approximations in bivariate renewal theory

Omey

Mitov²,

Vesilo³

2018

Publ Inst Math (Belgr)

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“…It appears that the only case where closed form expansions are available are when F is Matrix exponential distributed, in which case an expression of U (x) is given in Asmussen and Bladt [3]. Mitov and Omey [18] provide heuristics on many terms asymptotics of U (x) that are verified on the already known cases. However, as the authors point out, those interesting expansions are only given formally and are not proved.…”

Section: Introductionmentioning

confidence: 99%