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Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process

Yıl 2017, Cilt: 5 Sayı: 4, 165 - 171, 01.10.2017

Öz

One of the important problems of stochastic process theory is to define the Laplace transformations for the distribution of this process. With this purpose, we will investigate a semi-Markov random processes with positive tendency and negative jump in this article. The first falling moment into the zero-level of this process is constructed as mathematically and the Laplace transformation of this random variable is obtained.

Kaynakça

  • Afanas’eva, L. G., Bulinskaya, E. V., ’Some asymptotical results for random walks in a strip’ Teor. Veroyatn. Primen. 29, 4, 658-668 (1983).
  • Borovkov, A. A., Stochastic Processes in The Theory of Queues, Nauka, Moscow 1972.
  • Borovkov A. A., ’On the asymptotic behaviour of the distributions of the first passage’, Mat. Zametki, Vol.75, No.1, pp.24-39, (2004).
  • Feller, W., An Introduction to Probability Theory and Its Applications, Vol. I, Wiley, New York 1968.
  • Gihman, I. I., Skorohod, A. V., The Theory of Stochastic Processes II, Springer-Verlag, 1975.
  • Lotov, V. I., On some boundary crossing problems for gaussian random walks, The Annals of Probab., 24, 1996, pp.2154-2171, (1996).
  • Lotov, V. I., ’On the asymptotics of distributions in two-sided boundary problems for random walks defined on a Markov chain’, Sib. Adv. Math. 1, 3, 26-51 (1991).
  • Nasirova, T. H, Karimova ,U. Y., ’Definition of Laplace transform of the first passage of zero level of the semimarkov random process with positive tendency and negative jump2, Applied mathematics, 2, pp. 908-912, (2011).
  • Nasirova, T. I., and Shamilova, B. G., ’Investigation of Some Probabilistic Characteristics of One Class of Semi Markov Wandering with Delaying Screens’, Automatic Control and Computer Sciences, Vol. 48, No. 2, 109-119 (2014).
  • Nasirova, T. I., Sadikova, R. I., and Ibaev, E. A., ’Determination of the Mean and Mean Square Deviations of the System Level’, Automatic Control and Computer Sciences, Vol. 49, No. 1, 37-45 (2015).
  • Omarova, K. K., Bakhshiev, S. B., ’The Laplace Transform for the Distribution of the Lower Bound Functional in a Semi Markov Walk Process with a Delay Screen at Zero’, Automatic Control and Computer Sciences, Vol. 44, No. 4, 246-252 (2010).
  • Omarova, K. K., ’Laplace transformation of ergodic distribution of the step process of semi-markov random walk with delaying screen at positive point’, The Third International Conference "Problems of Cybernetics and Informatics", (2010).
  • Prabhu, N. U., Stochastic Storage Processes, New York, Springer-Verlag, 1981.
  • Spitzer, F., Principles of Random Walk, Van Nostrand, Princeton, 1969.
Yıl 2017, Cilt: 5 Sayı: 4, 165 - 171, 01.10.2017

Öz

Kaynakça

  • Afanas’eva, L. G., Bulinskaya, E. V., ’Some asymptotical results for random walks in a strip’ Teor. Veroyatn. Primen. 29, 4, 658-668 (1983).
  • Borovkov, A. A., Stochastic Processes in The Theory of Queues, Nauka, Moscow 1972.
  • Borovkov A. A., ’On the asymptotic behaviour of the distributions of the first passage’, Mat. Zametki, Vol.75, No.1, pp.24-39, (2004).
  • Feller, W., An Introduction to Probability Theory and Its Applications, Vol. I, Wiley, New York 1968.
  • Gihman, I. I., Skorohod, A. V., The Theory of Stochastic Processes II, Springer-Verlag, 1975.
  • Lotov, V. I., On some boundary crossing problems for gaussian random walks, The Annals of Probab., 24, 1996, pp.2154-2171, (1996).
  • Lotov, V. I., ’On the asymptotics of distributions in two-sided boundary problems for random walks defined on a Markov chain’, Sib. Adv. Math. 1, 3, 26-51 (1991).
  • Nasirova, T. H, Karimova ,U. Y., ’Definition of Laplace transform of the first passage of zero level of the semimarkov random process with positive tendency and negative jump2, Applied mathematics, 2, pp. 908-912, (2011).
  • Nasirova, T. I., and Shamilova, B. G., ’Investigation of Some Probabilistic Characteristics of One Class of Semi Markov Wandering with Delaying Screens’, Automatic Control and Computer Sciences, Vol. 48, No. 2, 109-119 (2014).
  • Nasirova, T. I., Sadikova, R. I., and Ibaev, E. A., ’Determination of the Mean and Mean Square Deviations of the System Level’, Automatic Control and Computer Sciences, Vol. 49, No. 1, 37-45 (2015).
  • Omarova, K. K., Bakhshiev, S. B., ’The Laplace Transform for the Distribution of the Lower Bound Functional in a Semi Markov Walk Process with a Delay Screen at Zero’, Automatic Control and Computer Sciences, Vol. 44, No. 4, 246-252 (2010).
  • Omarova, K. K., ’Laplace transformation of ergodic distribution of the step process of semi-markov random walk with delaying screen at positive point’, The Third International Conference "Problems of Cybernetics and Informatics", (2010).
  • Prabhu, N. U., Stochastic Storage Processes, New York, Springer-Verlag, 1981.
  • Spitzer, F., Principles of Random Walk, Van Nostrand, Princeton, 1969.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Selahattin Maden

Ulviyya Y. Karimova Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 4

Kaynak Göster

APA Maden, S., & Karimova, U. Y. (2017). Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process. New Trends in Mathematical Sciences, 5(4), 165-171.
AMA Maden S, Karimova UY. Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process. New Trends in Mathematical Sciences. Ekim 2017;5(4):165-171.
Chicago Maden, Selahattin, ve Ulviyya Y. Karimova. “Determination of the Laplace Transform for the First Falling Moment to Zero Level of a Semi-Markov Random Process”. New Trends in Mathematical Sciences 5, sy. 4 (Ekim 2017): 165-71.
EndNote Maden S, Karimova UY (01 Ekim 2017) Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process. New Trends in Mathematical Sciences 5 4 165–171.
IEEE S. Maden ve U. Y. Karimova, “Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process”, New Trends in Mathematical Sciences, c. 5, sy. 4, ss. 165–171, 2017.
ISNAD Maden, Selahattin - Karimova, Ulviyya Y. “Determination of the Laplace Transform for the First Falling Moment to Zero Level of a Semi-Markov Random Process”. New Trends in Mathematical Sciences 5/4 (Ekim 2017), 165-171.
JAMA Maden S, Karimova UY. Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process. New Trends in Mathematical Sciences. 2017;5:165–171.
MLA Maden, Selahattin ve Ulviyya Y. Karimova. “Determination of the Laplace Transform for the First Falling Moment to Zero Level of a Semi-Markov Random Process”. New Trends in Mathematical Sciences, c. 5, sy. 4, 2017, ss. 165-71.
Vancouver Maden S, Karimova UY. Determination of the laplace transform for the first falling moment to zero level of a semi-Markov random process. New Trends in Mathematical Sciences. 2017;5(4):165-71.