Ingtegral equations with delaying arguments for semi-Markovian processes

Year 2017, Volume: 5 Issue: 3, 162 - 167, 01.07.2017

Selahattin Maden , Ulviyya Y. Karimova Tamilla İ. Nasirova

https://izlik.org/JA96PS99DH

Abstract

In this paper, the Laplace transform of the distribution of the duration of a particular semi-Markovian random walk period is obtained in the form of the difference equation.

Keywords

Laplace transforms , semi-Markovian random process , random variable , process with positive tendency and negative jumps

References

• Borovkov, A. A. (1976). Stochastic Processes in Queueing Theory, Springer Verlag, New York.
• Busarov, V. A. (2004). On asymptotic behaviour of random wanderings in random medium with delaying screen, Vest. Mos. Gos. Univ., 1(5), 61-63.
• Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. I, Wiley, New York.
• Khaniev, T.A., Unver, I. (1997). The study of the level zero crossing time of a semi-Markovian random walk with delaying screen, Turkish J. Mathematics, 2(1), 257–268.
• Lotov, V. I. (1991a). On random walks in a band. Probability Theory and its Application, 36(1), 160-165.
• Lotov, V. I. (1991b). On the asymptotic of distributions in two-sided boundary problems for random walks defined on a markov chain, Sib. Adv. Math., 1(2), 26-51.
• Nasirova, . I. (1984). Processes of Semi-Markov Random Walk, ELM, Baku, 165p.
• Nasirova,. I., Ibayev, E. A., Aliyeva, T.A. (2005). The Laplace transformation of the distribution of the first moment reaching the positive delaying screen with the semi-Markovian process, Proc. Int. Conf. On Modern Problems and New Trends in Probability Theory, Chernivtsi, Ukraine, 19-26.
• Nasirova, I., Omarova, K. K. (2007). Distribution of the lower boundary functional of the step process of semi-Markov random walk with delaying screen at zero, Automatic Control and Computer Sciences, 59(7), 1010-1018.
• Omarova, K. K., Bakhshiev, Sh. B. (2010). 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, 44(4), 246–252.
• Unver, I., Tundzh, Ya. S., Ibaev, E. (2014). Laplace–Stieltjes transform of distribution of the first moment of crossing the level a(a > 0) by a semi-Markovian random walk with positive drift and negative jmps, Automatic Control and Computer Sciences, 48(3), 144–149.