Functional limit theorems for critical processes with immigration

DOI10.1239/aap/1198177239zbMath1205.60150OpenAlexW2034502416MaRDI QIDQ5443151

Ibrahim Rahimov

Publication date: 20 February 2008

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1198177239

zbMATH Keywords

branching processimmigrationmartingale limit theorem

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Stochastic processes (60G99) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items

Homogeneous branching processes with non-homogeneous immigration, Some Asymptotic Results for Strongly Critical Branching Processes with Immigration in Varying Environment, Conditional Least Squares Estimators for the Offspring Mean in a Subcritical Branching Process with Immigration, On asymptotics of branching processes with immigration, A note on asymptotic behavior of critical Galton-Watson processes with immigration, On the asymptotic behavior of a subcritical branching process with immigration, Asymptotic distributions for weighted estimators of the offspring mean in a branching process, Nearly unstable integer‐valued ARCH process and unit root testing, A fluctuation limit theorem for a critical branching process with dependent immigration, Variance Estimators in Critical Branching Processes With Non-Homogeneous Immigration, Asymptotic distribution of the CLSE in a critical process with immigration, Validity of the bootstrap in the critical process with a non-stationary immigration, Estimation of the offspring mean in a supercritical branching process with non-stationary immigration, Branching processes in varying environment with generation-dependent immigration, Asymptotically Normal Estimators for the Offspring Mean in the Branching Process with Immigration, Bootstrap of the offspring mean in the critical process with a non-stationary immigration

Cites Work

• Some asymptotic results for the branching process with immigration
• Invalidity of bootstrap for critical branching processes with immigration
• Random sums and branching stochastic processes
• An integer-valued pth-order autoregressive structure (INAR(p)) process
• Asymptotic inference for nearly unstable INAR(1) models
• Limit theorems for some functionals of certain Galton-Watson branching processes
• The Limit of a Sequence of Branching Processes
• Convergence of critical Galton-Watson branching processes
• Fluctuation limit of branching processes with immigration and estimation of the means
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