Small deviations for critical Galton-Watson processes with infinite variance

2025/05/15 by Vladimir Vatutin, Vatutin, Vladimir, Elena Dyakonova +3
Mathematics · Physics and Astronomy · #60F10 #60J80 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2505.10137

openalex publication_date 2025/05/15 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of small deviation probabilities for the critical Galton-Watson processes with infinite variance of the offspring sizes of particles and apply the obtained result to investigate the structure of a reduced critical Galton-Watson process.

Citations

• The coalescent structure of multitype continuous-time Galton-Watson trees
• The coalescent structure of continuous-time Galton-Watson trees
• Reduced branching processes with very heavy tails

Related

• Reduced critical processes for small populations
• Lower deviation probabilities for supercritical Galton-Watson processes
• On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration
• Small deviations of a Galton-Watson process with immigration
• On the scaling limits of Galton Watson processes in varying environment