On Long-time Behaviors of States of Galton-Watson Branching Processes Allowing Immigration

Imomov, Azam A.

doi:10.17516/1997-1397-2015-8-4-394-405

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Invariant Measures Of Gwpi1

Introduction1

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Cited by 4 publications

(2 citation statements)

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“…Remark 1. The analogous result as in Theorem 2 has been proved in [5] provided that δ = 1 and f ′′′ (1−) < ∞.…”

Section: Invariant Measures Of Gwpisupporting

confidence: 68%

On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration

Imomov¹,

Tukhtaev²

2019

Preprint

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“…Remark 1. The analogous result as in Theorem 2 has been proved in [5] provided that δ = 1 and f ′′′ (1−) < ∞.…”

Section: Invariant Measures Of Gwpisupporting

confidence: 68%

On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration

Imomov¹,

Tukhtaev²

2019

Preprint

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“…56-60]) The Q-process was considered first by Lamperti and Ney [14]. Some properties of it were discussed by Pakes [15][16][17], Imomov [7,[9][10][11], Formanov and Imomov [4]. A considerable part of the paper [12] is devoted to the discussion of this process from the viewpoint of branching transformation called the Lamperti-Ney transformation.…”

Section: Introductionmentioning

confidence: 99%

On the Limit Structure of Continuous-time Markov Branching Process

Imamov¹,

Imomov²

2017

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

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On Asymptotic Structure of the Critical Galton–Watson Branching Processes with Infinite Variance and Allowing Immigration

Imomov¹,

Tukhtaev²

2021

Applied Modeling Techniques and Data Analysis 2

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Consider the critical Galton-Watson branching system with infinite variance of the offspring law. We provide an alternative arguments against what Slack [9] did when it seeked for a local expression in the neighborhood of point 1 of the generating function for invariant measures of the branching system. So, we obtain the global expression for all s ∈ [0,1) of this generating function. A fundamentally improved version of the differential analogue of the Basic Lemma of the theory of critical branching systems is established. This assertion plays a key role in the formulation of the local limit theorem with explicit terms in the asymptotic expansion of local probabilities. We also determine the decay rate of the remainder term in this expansion.

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On Long-time Behaviors of States of Galton-Watson Branching Processes Allowing Immigration

Abstract: We observe the discrete-time Branching Process allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. In the critical situation a speed of this convergence is defined.

Cited by 4 publications

References 15 publications

On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration

On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration

On the Limit Structure of Continuous-time Markov Branching Process

On Asymptotic Structure of the Critical Galton–Watson Branching Processes with Infinite Variance and Allowing Immigration

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