TY - JOUR T1 - On a conditioned Limit Structure of the Markov Branching Process AU - Imomov, Azam PY - 2017 DA - March JF - International Journal of Applied Mathematics Electronics and Computers PB - PLUSBASE AKADEMİ ORGANİZASYON VE DANIŞMANLIK WT - DergiPark SN - 2147-8228 SP - 25 EP - 28 VL - 5 IS - 1 LA - en AB - 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. KW - Markov Branching processes KW - Markov Q-processes KW - transition function KW - q-matrix KW - limit theorems CR - Anderson, W.(1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. New York: Springer. CR - Athreya, K.B. and Ney, P.E.(1972). Branching processes. New York: Springer. CR - Formanov, Sh.K. and Imomov, A.A.(2011). On asymptotic properties of Q-processes. Uzbek Mathematical Journal, 3, 175-183. (in Russian) CR - 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. CR - 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. CR - Imomov, A.A.(2012). On Markov analogue of Q-processes with continuous time. Theory of Probability and Mathematical Statistics, 84, 57-64. CR - 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. CR - 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. CR - Kolmogorov, A.N and Dmitriev, N.A.(1947). Branching stochastic process. Reports of Academy of Sciences of USSR, 56, 7-10. (Russian) CR - Lamperti, J. and Ney, P.E.(1968). Conditioned branching processes and their limiting diffusions. Theory of Probability and its Applications, 13, 126-137. CR - Nagaev, A.V. and Badalbaev, I.S.(1967). A refinement of certain theorems on branching random process. Litovskiy Matematicheskiy Sbornik, 7(1), 129-136. CR - Pakes, A.G.(2010). Critical Markov branching process limit theorems allowing infinite variance. Advances in Applied Probability, 42, 460-488. CR - Pakes, A.G.(1999). Revisiting conditional limit theorems for the mortal simple branching process. Bernoulli, 5(6), 969-998. CR - Pakes, A.G.(1971). Some limit theorems for the total progeny of a branching process. Advances in Applied Probability, 3, 176-192. CR - Sevastyanov, B.A.(1951). The theory of Branching stochastic process. Uspekhi Matematicheskikh Nauk, 6(46), 47-99. (in Russian) CR - Sevastyanov, B.A.(1971). Branching processes, Moscow: Nauka. (Russian) CR - 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. UR - https://dergipark.org.tr/en/pub/ijamec/issue//450936 L1 - https://dergipark.org.tr/en/download/article-file/519250 ER -