On the Limit Structure of Continuous-time Markov Branching Process

Imamov, Azamat A.; Imomov, Azam A.

doi:10.17516/1997-1397-2017-10-1-117-127

Cited by 2 publications

(3 citation statements)

References 7 publications

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“…Among the random trajectories of branching systems, there are those that continue a long time. In the case of the GWB model, the class of such trajectories forms another stochastic model called Q-process; see [2] and [6]. In the case of continuous-time Markov branching systems, an analogous model called the Markov Q-process, was first introduced in [5].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Limit Theorems for the Positive Recurrent Q-process

Imomov

Nazarov²

2023

Communications in Computer and Information Science

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We examine the population growth system called Q-processes. This is defined by the Galton-Watson Branching system conditioned on non-extinction of its trajectory in the remote future. In this paper we observe the total progeny up to time n in the Q-process. By analogy with branching systems, this variable is of great interest in studying the deep properties of the Q-process. We find that the sum total progeny as a random variable approximates the standard normal distribution function under a second moment assumption for the initial Galton-Watson system offspring law. We estimate the speed rate of this approximation.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Limit Theorems for the Positive Recurrent Q-process

Imomov

Nazarov²

2023

Communications in Computer and Information Science

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“…And we get another population process called Markov Q-process instead of MBPI. We refer the reader to [4] and [6] for the details on the Markov Q-process; see also [1, pp. 56-58] and [8] for the discrete-time case.…”

Section: Put Into Consideration Gfmentioning

confidence: 99%

“…Put R(t; s) := 1 − F(t; s). The following result called the Basic lemma of the theory of critical Markov branching processes, has been proved in [4]. We provide it in slightly different form below, taking from its proof.…”

Section: Auxiliariesmentioning

confidence: 99%

On Estimation of the Convergence Rate to Invariant Measures in Markov Branching Processes with Possibly Infinite Variance and Allowing Immigration

Imomov¹

2021

J. Sib. Fed. Univ., Math. phys.

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The paper discusses the continuous-time Markov Branching Process allowing Immigration. We are considering a critical case for which the second moment of offspring law and the first moment of immigration law are possibly infinite. Assuming that the nonlinear parts of the appropriate generating functions are regularly varying in the sense of Karamata, we prove theorems on convergence of transition functions of the process to invariant measures. We deduce the speed rate of these convergence providing that slowly varying factors are with remainder

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On the Limit Structure of Continuous-time Markov Branching Process

Cited by 2 publications

References 7 publications

Limit Theorems for the Positive Recurrent Q-process

Limit Theorems for the Positive Recurrent Q-process

On Estimation of the Convergence Rate to Invariant Measures in Markov Branching Processes with Possibly Infinite Variance and Allowing Immigration

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