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Ingtegral equations with delaying arguments for semi-Markovian processes

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

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.

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

Abstract

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.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Selahattin Maden

Ulviyya Y. Karimova This is me

Tamilla İ. Nasirova This is me

Publication Date July 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA 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.