Berry-Esseen bound for nearly critical branching processes with immigration

Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics ◽

10.17721/1812-5409.2019/4.5 ◽

2019 ◽

pp. 42-49

Author(s):

Ya. Khusanbaev ◽

S. Sharipov ◽

V. Golomoziy

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Rate Of Convergence ◽

Central Limit ◽

Branching Process ◽

Branching Processes ◽

Branching Process With Immigration ◽

Critical Branching Process

In this paper, we consider a nearly critical branching process with immigration. We obtain the rate of convergence in central limit theorem for nearly critical branching processes with immigration.

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Central limit theorem for branching process with immigration

10.1063/5.0057214 ◽

2021 ◽

Author(s):

Sadillo O. Sharipov

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Branching Process ◽

Branching Process With Immigration

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Remark on the rate of convergence in the random central limit theorem for mixing sequences

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ◽

10.1007/bf00539440 ◽

1975 ◽

Vol 31 (2) ◽

pp. 157-160 ◽

Cited By ~ 9

Author(s):

B. L. S. Prakasa Rao

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Rate Of Convergence ◽

Central Limit ◽

Mixing Sequences

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Non-Classical Estimates of the Rate of Convergence in the Multi-Dimensional Central Limit Theorem. II

Theory of Probability and Its Applications ◽

10.1137/1123004 ◽

1978 ◽

Vol 23 (1) ◽

pp. 50-62 ◽

Cited By ~ 3

Author(s):

V. I. Rotar’

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Rate Of Convergence ◽

Central Limit

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Rate of convergence in the central limit theorem in the space D[0, 1]

Lithuanian Mathematical Journal ◽

10.1007/bf00972120 ◽

1989 ◽

Vol 28 (3) ◽

pp. 229-238 ◽

Cited By ~ 2

Author(s):

V. Paulauskas ◽

D. Jukneviciene

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Rate Of Convergence ◽

Central Limit ◽

The Central Limit Theorem

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On the estimate of the rate of convergence in the central limit theorem in Hilbert space

Stability Problems for Stochastic Models - Lecture Notes in Mathematics ◽

10.1007/bfb0084183 ◽

1989 ◽

pp. 309-327 ◽

Cited By ~ 1

Author(s):

V. V. Senatov

Keyword(s):

Hilbert Space ◽

Central Limit Theorem ◽

Limit Theorem ◽

Rate Of Convergence ◽

Central Limit ◽

The Central Limit Theorem

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On the rate of convergence of moments in the central limit theorem in Hilbert space

Lecture Notes in Mathematics - Probability Theory and Mathematical Statistics ◽

10.1007/bfb0072951 ◽

1983 ◽

pp. 561-575 ◽

Cited By ~ 1

Author(s):

V. V. Sazonov ◽

B. A. Zalesskii

Keyword(s):

Hilbert Space ◽

Central Limit Theorem ◽

Limit Theorem ◽

Rate Of Convergence ◽

Central Limit ◽

The Central Limit Theorem ◽

Convergence Of Moments

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On estimation of the variances for critical branching processes with immigration

Journal of Applied Probability ◽

10.1017/s0021900200006793 ◽

2010 ◽

Vol 47 (02) ◽

pp. 526-542

Author(s):

Chunhua Ma ◽

Longmin Wang

Keyword(s):

Least Squares ◽

Branching Process ◽

Branching Processes ◽

Limiting Distributions ◽

Least Squares Estimators ◽

Conditional Least Squares ◽

Regularly Varying ◽

Branching Process With Immigration ◽

Critical Branching Process

The conditional least-squares estimators of the variances are studied for a critical branching process with immigration that allows the offspring distributions to have infinite fourth moments. We derive different forms of limiting distributions for these estimators when the offspring distributions have regularly varying tails with index α. In particular, in the case in which 2 < α < 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √n, which is different from that of Winnicki (1991).

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