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On a conditioned Limit Structure of the Markov Branching Process

Year 2017, Volume: 5 Issue: 1, 25 - 28, 31.03.2017

Abstract

The principal aims are to investigate asymptotic properties of the stochastic population process as a continuous-time Markov chain called Markov Q-Process. We investigate asymptotic properties of the transition probabilities of the Markov Q-Process and their convergence to stationary measures.

References

  • Anderson, W.(1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. New York: Springer.
  • Athreya, K.B. and Ney, P.E.(1972). Branching processes. New York: Springer.
  • Formanov, Sh.K. and Imomov, A.A.(2011). On asymptotic properties of Q-processes. Uzbek Mathematical Journal, 3, 175-183. (in Russian)
  • Heatcote, C.R., Seneta E. and Vere-Jones.(1967). A refinement of two theorems in the theory of branching process. Theory of Probab. and its Appl., 12(2), 341-346.
  • Imomov, A.A.(2014). On long-term behavior of continuous-time Markov Branching Processes allowing Immigration. Journal of Siberian Federal University. Mathematics and Physics, 7(4), 429-440.
  • Imomov, A.A.(2012). On Markov analogue of Q-processes with continuous time. Theory of Probability and Mathematical Statistics, 84, 57-64.
  • Imomov, A.A.(2005). A differential analog of the main lemma of the theory of Markov branching processes and its applications. Ukrainian Math. Journal, 57(2), 307–315.
  • Imomov, A.A.(2002). Some asymptotical behaviors of Galton-Watson branching processes under condition of non-extinctinity of it remote future. Abstracts of Comm. of 8th Vilnius Conference: Probab. Theory and Math. Statistics, Vilnius, Lithuania, p.118.
  • Kolmogorov, A.N and Dmitriev, N.A.(1947). Branching stochastic process. Reports of Academy of Sciences of USSR, 56, 7-10. (Russian)
  • Lamperti, J. and Ney, P.E.(1968). Conditioned branching processes and their limiting diffusions. Theory of Probability and its Applications, 13, 126-137.
  • Nagaev, A.V. and Badalbaev, I.S.(1967). A refinement of certain theorems on branching random process. Litovskiy Matematicheskiy Sbornik, 7(1), 129-136.
  • Pakes, A.G.(2010). Critical Markov branching process limit theorems allowing infinite variance. Advances in Applied Probability, 42, 460-488.
  • Pakes, A.G.(1999). Revisiting conditional limit theorems for the mortal simple branching process. Bernoulli, 5(6), 969-998.
  • Pakes, A.G.(1971). Some limit theorems for the total progeny of a branching process. Advances in Applied Probability, 3, 176-192.
  • Sevastyanov, B.A.(1951). The theory of Branching stochastic process. Uspekhi Matematicheskikh Nauk, 6(46), 47-99. (in Russian)
  • Sevastyanov, B.A.(1971). Branching processes, Moscow: Nauka. (Russian)
  • Zolotarev, V.M.(1957). More exact statements of several theorems in the theory of branching processes. Theory of Probability and its Applications, 2, 245-253.
Year 2017, Volume: 5 Issue: 1, 25 - 28, 31.03.2017

Abstract

References

  • Anderson, W.(1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. New York: Springer.
  • Athreya, K.B. and Ney, P.E.(1972). Branching processes. New York: Springer.
  • Formanov, Sh.K. and Imomov, A.A.(2011). On asymptotic properties of Q-processes. Uzbek Mathematical Journal, 3, 175-183. (in Russian)
  • Heatcote, C.R., Seneta E. and Vere-Jones.(1967). A refinement of two theorems in the theory of branching process. Theory of Probab. and its Appl., 12(2), 341-346.
  • Imomov, A.A.(2014). On long-term behavior of continuous-time Markov Branching Processes allowing Immigration. Journal of Siberian Federal University. Mathematics and Physics, 7(4), 429-440.
  • Imomov, A.A.(2012). On Markov analogue of Q-processes with continuous time. Theory of Probability and Mathematical Statistics, 84, 57-64.
  • Imomov, A.A.(2005). A differential analog of the main lemma of the theory of Markov branching processes and its applications. Ukrainian Math. Journal, 57(2), 307–315.
  • Imomov, A.A.(2002). Some asymptotical behaviors of Galton-Watson branching processes under condition of non-extinctinity of it remote future. Abstracts of Comm. of 8th Vilnius Conference: Probab. Theory and Math. Statistics, Vilnius, Lithuania, p.118.
  • Kolmogorov, A.N and Dmitriev, N.A.(1947). Branching stochastic process. Reports of Academy of Sciences of USSR, 56, 7-10. (Russian)
  • Lamperti, J. and Ney, P.E.(1968). Conditioned branching processes and their limiting diffusions. Theory of Probability and its Applications, 13, 126-137.
  • Nagaev, A.V. and Badalbaev, I.S.(1967). A refinement of certain theorems on branching random process. Litovskiy Matematicheskiy Sbornik, 7(1), 129-136.
  • Pakes, A.G.(2010). Critical Markov branching process limit theorems allowing infinite variance. Advances in Applied Probability, 42, 460-488.
  • Pakes, A.G.(1999). Revisiting conditional limit theorems for the mortal simple branching process. Bernoulli, 5(6), 969-998.
  • Pakes, A.G.(1971). Some limit theorems for the total progeny of a branching process. Advances in Applied Probability, 3, 176-192.
  • Sevastyanov, B.A.(1951). The theory of Branching stochastic process. Uspekhi Matematicheskikh Nauk, 6(46), 47-99. (in Russian)
  • Sevastyanov, B.A.(1971). Branching processes, Moscow: Nauka. (Russian)
  • Zolotarev, V.M.(1957). More exact statements of several theorems in the theory of branching processes. Theory of Probability and its Applications, 2, 245-253.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Azam Imomov

Publication Date March 31, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Imomov, A. (2017). On a conditioned Limit Structure of the Markov Branching Process. International Journal of Applied Mathematics Electronics and Computers, 5(1), 25-28.
AMA Imomov A. On a conditioned Limit Structure of the Markov Branching Process. International Journal of Applied Mathematics Electronics and Computers. March 2017;5(1):25-28.
Chicago Imomov, Azam. “On a Conditioned Limit Structure of the Markov Branching Process”. International Journal of Applied Mathematics Electronics and Computers 5, no. 1 (March 2017): 25-28.
EndNote Imomov A (March 1, 2017) On a conditioned Limit Structure of the Markov Branching Process. International Journal of Applied Mathematics Electronics and Computers 5 1 25–28.
IEEE A. Imomov, “On a conditioned Limit Structure of the Markov Branching Process”, International Journal of Applied Mathematics Electronics and Computers, vol. 5, no. 1, pp. 25–28, 2017.
ISNAD Imomov, Azam. “On a Conditioned Limit Structure of the Markov Branching Process”. International Journal of Applied Mathematics Electronics and Computers 5/1 (March 2017), 25-28.
JAMA Imomov A. On a conditioned Limit Structure of the Markov Branching Process. International Journal of Applied Mathematics Electronics and Computers. 2017;5:25–28.
MLA Imomov, Azam. “On a Conditioned Limit Structure of the Markov Branching Process”. International Journal of Applied Mathematics Electronics and Computers, vol. 5, no. 1, 2017, pp. 25-28.
Vancouver Imomov A. On a conditioned Limit Structure of the Markov Branching Process. International Journal of Applied Mathematics Electronics and Computers. 2017;5(1):25-8.