verifiedOpen Access Peer-Reviewed Scientific Journal (CC BY 4.0)
Peer-Reviewed Academic JournalInternational Journal of Applied Methods in Electronics and Computers
ISSN: 3023-4409DOI Prefix: 10.58190/ijamec
search
person
Research ArticlesverifiedPeer-ReviewedOpen Access
Pages: 25-28

On a conditioned Limit Structure of the Markov Branching Process

Azam Imomov
Publication DateMarch 31, 2017
Volume / IssueVol. 5, No. 1 (pp. 25-28)
subject

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.
Keywords:Markov Branching processesMarkov Q-processestransition functionq-matrixlimit theorems
format_list_numbered

References (17)

Cited Literature
  1. 1

    Anderson, W.(1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. New York: Springer.

  2. 2

    Athreya, K.B. and Ney, P.E.(1972). Branching processes. New York: Springer.

  3. 3

    Formanov, Sh.K. and Imomov, A.A.(2011). On asymptotic properties of Q-processes. Uzbek Mathematical Journal, 3, 175-183. (in Russian)

  4. 4

    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.

  5. 5

    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.

  6. 6

    Imomov, A.A.(2012). On Markov analogue of Q-processes with continuous time. Theory of Probability and Mathematical Statistics, 84, 57-64.

  7. 7

    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.

  8. 8

    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.

  9. 9

    Kolmogorov, A.N and Dmitriev, N.A.(1947). Branching stochastic process. Reports of Academy of Sciences of USSR, 56, 7-10. (Russian)

  10. 10

    Lamperti, J. and Ney, P.E.(1968). Conditioned branching processes and their limiting diffusions. Theory of Probability and its Applications, 13, 126-137.

  11. 11

    Nagaev, A.V. and Badalbaev, I.S.(1967). A refinement of certain theorems on branching random process. Litovskiy Matematicheskiy Sbornik, 7(1), 129-136.

  12. 12

    Pakes, A.G.(2010). Critical Markov branching process limit theorems allowing infinite variance. Advances in Applied Probability, 42, 460-488.

  13. 13

    Pakes, A.G.(1999). Revisiting conditional limit theorems for the mortal simple branching process. Bernoulli, 5(6), 969-998.

  14. 14

    Pakes, A.G.(1971). Some limit theorems for the total progeny of a branching process. Advances in Applied Probability, 3, 176-192.

  15. 15

    Sevastyanov, B.A.(1951). The theory of Branching stochastic process. Uspekhi Matematicheskikh Nauk, 6(46), 47-99. (in Russian)

  16. 16

    Sevastyanov, B.A.(1971). Branching processes, Moscow: Nauka. (Russian)

  17. 17

    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.

format_quote

How to Cite This Article

A. I. (2017). On a conditioned Limit Structure of the Markov Branching Process. International Journal of Applied Methods in Electronics and Computers, 25-28.