BibTex RIS Kaynak Göster

On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance

Yıl 2013, Cilt: 42 Sayı: 3, 299 - 307, 01.03.2013

Öz

In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0. Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.

Kaynakça

  • Aliyev, R.T., Khaniyev, T.A and Kesemen, T. Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance, Communications in Statistics-Theory and Methods, 39 (1), 130–143, 2010.
  • Aliyev, R., Kucuk, Z. and Khaniyev, T. Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modelling, 34 (11), 3599–3607, 2010.
  • Anisimov, V.V. and Artalejo, J.R. Analysis of Markov multiserver retrial queues with negative arrivals, Queueing Systems: Theory and Applic, 39 (2/3), 157–182, 2001.
  • Borovkov, A.A. Stochastic Process in Queueing Theory, (Springer, New York, 1976) . Feller, W. Introduction to Probability Theory and Its Appl. II,( New York, 1971 ).
  • Gihman, I.I. and Skorohod, A.V. Theory of Stochastic Processes II, (Berlin, 1975 ).
  • Khaniyev, T.A. and Mammadova, Z. On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands, Journal of Statistical Computation and Simulation,76 (10), 861–874 , 2006.
  • Khaniyev, T.A., Kesemen, T., Aliyev, R.T. and Kokangul, A. Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance, Statistics & Probability Letters, 78 (6), 785–793, 2008.
  • Lotov, V.I. On some boundary crossing problems for Gaussian random walks, The Annals of Probability, 24 (4), 2154–2171, 1996.
  • Rogozin, B.A. On the distribution of the first jump, Theory Probability and Its Applications, 9 (3), 498–545, 1964.

On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance

Yıl 2013, Cilt: 42 Sayı: 3, 299 - 307, 01.03.2013

Öz

-

Kaynakça

  • Aliyev, R.T., Khaniyev, T.A and Kesemen, T. Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance, Communications in Statistics-Theory and Methods, 39 (1), 130–143, 2010.
  • Aliyev, R., Kucuk, Z. and Khaniyev, T. Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modelling, 34 (11), 3599–3607, 2010.
  • Anisimov, V.V. and Artalejo, J.R. Analysis of Markov multiserver retrial queues with negative arrivals, Queueing Systems: Theory and Applic, 39 (2/3), 157–182, 2001.
  • Borovkov, A.A. Stochastic Process in Queueing Theory, (Springer, New York, 1976) . Feller, W. Introduction to Probability Theory and Its Appl. II,( New York, 1971 ).
  • Gihman, I.I. and Skorohod, A.V. Theory of Stochastic Processes II, (Berlin, 1975 ).
  • Khaniyev, T.A. and Mammadova, Z. On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands, Journal of Statistical Computation and Simulation,76 (10), 861–874 , 2006.
  • Khaniyev, T.A., Kesemen, T., Aliyev, R.T. and Kokangul, A. Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance, Statistics & Probability Letters, 78 (6), 785–793, 2008.
  • Lotov, V.I. On some boundary crossing problems for Gaussian random walks, The Annals of Probability, 24 (4), 2154–2171, 1996.
  • Rogozin, B.A. On the distribution of the first jump, Theory Probability and Its Applications, 9 (3), 498–545, 1964.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Matematik
Yazarlar

Tülay Kesemen Bu kişi benim

Yayımlanma Tarihi 1 Mart 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 42 Sayı: 3

Kaynak Göster

APA Kesemen, T. (2013). On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance. Hacettepe Journal of Mathematics and Statistics, 42(3), 299-307.
AMA Kesemen T. On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance. Hacettepe Journal of Mathematics and Statistics. Mart 2013;42(3):299-307.
Chicago Kesemen, Tülay. “On the Semi-Markovian Random Walk With Delay AndWeibull Distributed Interference of Chance”. Hacettepe Journal of Mathematics and Statistics 42, sy. 3 (Mart 2013): 299-307.
EndNote Kesemen T (01 Mart 2013) On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance. Hacettepe Journal of Mathematics and Statistics 42 3 299–307.
IEEE T. Kesemen, “On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance”, Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 3, ss. 299–307, 2013.
ISNAD Kesemen, Tülay. “On the Semi-Markovian Random Walk With Delay AndWeibull Distributed Interference of Chance”. Hacettepe Journal of Mathematics and Statistics 42/3 (Mart 2013), 299-307.
JAMA Kesemen T. On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance. Hacettepe Journal of Mathematics and Statistics. 2013;42:299–307.
MLA Kesemen, Tülay. “On the Semi-Markovian Random Walk With Delay AndWeibull Distributed Interference of Chance”. Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 3, 2013, ss. 299-07.
Vancouver Kesemen T. On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance. Hacettepe Journal of Mathematics and Statistics. 2013;42(3):299-307.