Limit distribution for a semi-Markovian random walk with Weibull distributed interference of chance

Kesemen, Tülay; Aliyev, Rovshan; Khaniyev, Tahir

doi:10.1186/1029-242x-2013-134

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…One of the most popular methods to obtain useful formulas for mentioned characteristics is using asymptotic expansion method. In recent years, many researchers have extensively studied the characteristics of an inventory model type (s,S) by using asymptotic approach (see Smith (1959), Feller (1971), Khaniyev and Aksop (2011), Aliyev and Khaniyev (2014), Kesemen et. al.…”

Section: Introductionmentioning

confidence: 99%

Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance

Kamişlik¹,

Kesemen²,

Khaniyev³

2019

Braz. J. Probab. Stat.

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In this study, a stochastic process X(t), which describes an inventory model of type (s,S) is considered in the presence of heavy tailed demands with infinite variance. The aim of this study is observing the impact of regularly varying demand distributions with infinite variance on the stochastic process X(t). The main motivation of this work is, the publication by Geluk (1997) where he provided a special asymptotic expansion for renewal function generated by regularly varying random variables. Two term asymptotic expansion for the ergodic distribution function of the process X(t) is obtained based on the main results proposed by Geluk (1997). Finally weak convergence theorem for the ergodic distribution of this process is proved by using Karamata theory.MSC 2010 subject classifications: Primary 60K05; secondary 60K20

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Section: Introductionmentioning

confidence: 99%

Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance

Kamişlik¹,

Kesemen²,

Khaniyev³

2019

Braz. J. Probab. Stat.

Self Cite

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Limit Theorem for a Semi-Markovian Random Walk with General Interference of Chance

Khaniyev¹,

Sevinc²

2020

jsm

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Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

Gever,

Khanıyev

2024

Gazi University Journal of Science

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In this study, a random walk process with generalized reflecting barrier is considered and an inequality for rate of weak convergence of the stationary distribution of the process of interest is propounded. Though the rate of convergence is not thoroughly examined, the literature does provide a weak convergence theorem under certain conditions for the stationary distribution of the process under consideration. Nonetheless, one of the most crucial issues in probability theory is the convergence rate in limit theorems, as it affects the precision and effectiveness of using these theorems in practice. Therefore, for the rate of convergence for the examined process, comparatively simple inequality is represented. The obtained inequality demonstrates that the rate of convergence is correlated with the tail of the distribution of ladder heights of the random walk.

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Limit distribution for a semi-Markovian random walk with Weibull distributed interference of chance

Cited by 3 publications

References 10 publications

Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance

Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance

Limit Theorem for a Semi-Markovian Random Walk with General Interference of Chance

Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

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