A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications

2009/06/15 by Chunhua Ma, Ma, Chunhua
Computer Science · Mathematics · #60H20 #60J35 #60J80 #60K37 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0906.2586

openalex publication_date 2009/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive Levy process. As applications of this result, we obtain some asymptotic estimates for the conditional least-squares estimator of the offspring means and variances of the offspring and immigration distributions.

Citations

• Stochastic equations of non-negative processes with jumps

Related

• Limit Theorems for Branching Processes with Immigration in a Random Environment
• A critical branching process with immigration in random environment
• On functional limit theorems for branching processes with dependent immigration
• On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration
• Complete left-tail asymptotic for branching processes with immigration