Tail generating functions for Markov branching processes

2014/10/06 by Serik Sagitov, Sagitov, Serik
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1410.1497

arxiv created 2014/10/06 · openalex publication_date 2014/10/06 · arxiv updated 2014/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a concise self-contained presentation of known and new limit theorems for the one-type Markov branching processes with continuous time. The new streamlined proofs are based on what we call, the tail generating function approach. Our analysis focuses on the singularity points of the master integral equation for the probability generating functions of the current population size.

Related

• On asymptotic structure of continuous-time Markov Branching Processes allowing Immigration and without high-order moments
• Continuous-state branching processes
• Tail generating functions for extendable branching processes
• The asymptotic tails of limit distributions of continuous time Markov chains
• Renewed Limit Theorems for the discrete-time Branching Process and its Conditioned Limiting Law interpretation