On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands

Khaniyev, Tahir; Mammadova, Zulfiyya

doi:10.1080/10629360500109234

Cited by 19 publications

(10 citation statements)

References 7 publications

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“…Otherwise, several approximation formulas are offered for these kinds of problems in the literature (see, e.g., Refs. ). The approximation formulas are generally simpler and easier in application.…”

Section: Introductionmentioning

confidence: 97%

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An asymptotic approach for a semi‐Markovian inventory model of type (s, S)

Khaniyev

Kokangül

Aliyev

2012

Appl Stoch Models Bus & Ind

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In this study, we constructed a stochastic process (X.t// that expresses a semi-Markovian inventory model of type (s,S/ and it is shown that this process is ergodic under some weak conditions. Moreover, we obtained exact and asymptotic expressions for the n th order moments .n D 1; 2; 3; : : :/ of ergodic distribution of the process X.t/, as S s ! 1. Finally, we tested how close the obtained approximation formulas are to the exact expressions.

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Section: Introductionmentioning

confidence: 97%

“…There are many valuable studies on these processes in the literature (see, e.g., Refs. ). However, these studies are generally theoretical and they are not exactly helpful for solving concrete real‐world problems because of the complexity of their mathematical structure.…”

Section: Introductionmentioning

confidence: 97%

An asymptotic approach for a semi‐Markovian inventory model of type (s, S)

Khaniyev

Kokangül

Aliyev

2012

Appl Stoch Models Bus & Ind

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“…are given by means of random walk with various type of barriers. There exist some important studies on this topic in the literature (see, for example, Alsmeyer, 1991;Aras and Woodroofe, 1993;Borovkov, 1976;Brown and Solomon, 1975;Khaniev et al, 1998Khaniev et al, , 2001Khaniyev et al, 2008;Khaniyev and Kucuk, 2004;Khaniyev and Mammadova, 2006;Lotov, 1996;Nasirova et al, 1998;Rogozin, 1964;Skorohod and Slobodenyuk, 1970;Spitzer, 1964, etc.). In these studies, absorbing, delaying, reflecting, and other known barriers are usually used.…”

Section: Introductionmentioning

confidence: 97%

Asymptotic Expansions for the Moments of the Semi-Markovian Random Walk with Gamma Distributed Interference of Chance

Aliyev

Khaniyev

Kesemen

2009

Communications in Statistics - Theory and Methods

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In this study, a semi-Markovian random walk with a discrete interference of chance (X t ) is considered and under some weak assumptions the ergodicity of this process is discussed. The exact formulas for the first four moments of the ergodic distribution of the process X t are obtained when the random variable 1 , which describes a discrete interference of chance, has a gamma distribution with parameters > 1 > 0. Based on these results, the asymptotic expansions are obtained for the first four moments of the ergodic distribution of the process X t , as → 0. Furthermore, the asymptotic expansions for the skewness and kurtosis of the ergodic distribution of the process X t are established. Finally, it is discussed that the alternative estimations for the stationary characteristics of this process can be offered by using obtained asymptotic expansions.

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“…Numerous works (see, for example, [1][2][3][4][5][6][7][8][9][10][11]) are devoted to this model. The model is investigated with allowance for requirements of inventory theory, queuing theory, reliability theory, actuarial theory, etc.…”

Section: Introductionmentioning

confidence: 99%