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

Selahattin Maden , Ulviyya Y. Karimova

https://izlik.org/JA76HB42FG

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.

Anahtar Kelimeler

Semi-Markov process , Laplace transform

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.