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.
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.
Year 2017,
Volume: 5 Issue: 3, 162 - 167, 01.07.2017
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.
Maden, S., Karimova, U. Y., & Nasirova, T. İ. (2017). Ingtegral equations with delaying arguments for semi-Markovian processes. New Trends in Mathematical Sciences, 5(3), 162-167.
AMA
Maden S, Karimova UY, Nasirova Tİ. Ingtegral equations with delaying arguments for semi-Markovian processes. New Trends in Mathematical Sciences. July 2017;5(3):162-167.
Chicago
Maden, Selahattin, Ulviyya Y. Karimova, and Tamilla İ. Nasirova. “Ingtegral Equations With Delaying Arguments for Semi-Markovian Processes”. New Trends in Mathematical Sciences 5, no. 3 (July 2017): 162-67.
EndNote
Maden S, Karimova UY, Nasirova Tİ (July 1, 2017) Ingtegral equations with delaying arguments for semi-Markovian processes. New Trends in Mathematical Sciences 5 3 162–167.
IEEE
S. Maden, U. Y. Karimova, and T. İ. Nasirova, “Ingtegral equations with delaying arguments for semi-Markovian processes”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 162–167, 2017.
ISNAD
Maden, Selahattin et al. “Ingtegral Equations With Delaying Arguments for Semi-Markovian Processes”. New Trends in Mathematical Sciences 5/3 (July 2017), 162-167.
JAMA
Maden S, Karimova UY, Nasirova Tİ. Ingtegral equations with delaying arguments for semi-Markovian processes. New Trends in Mathematical Sciences. 2017;5:162–167.
MLA
Maden, Selahattin et al. “Ingtegral Equations With Delaying Arguments for Semi-Markovian Processes”. New Trends in Mathematical Sciences, vol. 5, no. 3, 2017, pp. 162-7.
Vancouver
Maden S, Karimova UY, Nasirova Tİ. Ingtegral equations with delaying arguments for semi-Markovian processes. New Trends in Mathematical Sciences. 2017;5(3):162-7.