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ABSTRACT: For a controlled branching process (CBP) with offspring distribution belonging to the power series family, the asymptotic normality of the posterior distribution of the basic parameter and the offspring mean is proved. As practical applications, we calculate asymptotic high probability density credibility sets for the offspring mean and we provide a rule to make inference about the value of this parameter. Moreover, the asymptotic posterior normality of the respective parameters of two classical branching models, namely the standard Galton–Watson process and the Galton–Watson process with immigration, is derived as particular cases of the CBP.
Statistics 08/2009; 43(4):367-378. · 0.72 Impact Factor
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Journal of Mathematical Sciences 01/2004; 121(5):2629-2635.
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ABSTRACT: This paper concerns the controlled branching process with random control function introduced by Yanev (Theor. Prob. Appl. 20 (1976) 421). Some relationships between its probability generating functions are established and the convergence in distribution of the population size to a nondegenerate and finite random variable is investigated.
Statistics [?] Probability Letters 01/2004; 67(3):277-284. · 0.50 Impact Factor
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ABSTRACT: The limit behaviour of a controlled branching process with random control function is investigated. A necessary condition and a sufficient condition for the geometric growth of such a process are established by considering the L<sup>1</sup>-convergence. Finally, taking into account the classical Xlog<sup>+</sup>X criterion in branching processes, a necessary and sufficient condition is provided.
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ABSTRACT: In this paper, the class of controlled branching processes with random control functions introduced by Yanev (1976) is considered. For this class, necessary and sufficient conditions are established for the process to become extinct with probability 1 and the limit probabilistic behaviour of the population size, suitably normed, is investigated.
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ABSTRACT: In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.
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ABSTRACT: Controlled branching processes (CBP) with a random control function provide a useful way to model generation sizes in population dynamics studies, where control on the growth of the population size is necessary at each generation. An important special case of this process is the well known branching process with immigration. Motivated by the work of Wei and Winnicki [C.Z. Wei, J. Winnicki, Estimation of the mean in the branching process with immigration, Ann. Statist. 18 (1990) 1757-1773], we develop a weighted conditional least squares estimator of the offspring mean of the CBP and derive the asymptotic limit distribution of the estimator when the process is subcritical, critical and supercritical. Moreover, we show the strong consistency of this estimator in all the cases. The results obtained here extend those of Wei and Winnicki [C.Z. Wei, J. Winnicki, Estimation of the mean in the branching process with immigration, Ann. Statist. 18 (1990) 1757-1773] for branching processes with immigration and provide a unified limit theory of estimation.
Stochastic Processes and their Applications 117(7):928-946. · 1.01 Impact Factor
