PreprintarXiv licencearXiv
Domains of Attraction for Quasi-Stationary Distributions of Branching Processes in Random Environments
Abstract
We obtain a complete characterization of the quasi-stationary distributions of subcritical stable continuous-state branching processes in Brownian random environments, together with the domain of attraction of each member. These distributions form a one-parameter family whose modified Laplace transforms are given explicitly in terms of Tricomi's confluent hypergeometric function. For every initial distribution, we determine whether the conditional law converges to a QSD and identify that QSD whenever it does. The necessary and sufficient criteria are formulated in terms of the tail probabilities and moments of the initial law.
Related
- Limit theorems for supercritical branching processes in Markovian environment with linear fractional offspring distributions
- Local Limit Theorem for Branching Processes in Varying Environments
- Convergence of stationary distributions for a class of zero-range processes and its application to a wealth distribution model with debt
- Quasi-stationary distributions and sharp metastable asymptotics for birth--death processes with a strong Allee effect
- Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels
BibTeX
@misc{li2026domains,
title = {{Domains of Attraction for Quasi-Stationary Distributions of Branching Processes in Random Environments}},
author = {Pei-Sen Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27122},
eprint = {2609.27122},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27122},
}
RIS
TY - UNPB
TI - Domains of Attraction for Quasi-Stationary Distributions of Branching Processes in Random Environments
AU - Pei-Sen Li
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27122
UR - https://arxiv.org/abs/2609.27122
AB - We obtain a complete characterization of the quasi-stationary distributions of subcritical stable continuous-state branching processes in Brownian random environments, together with the domain of attraction of each member. These distributions form a one-parameter family whose modified Laplace transforms are given explicitly in terms of Tricomi's confluent hypergeometric function. For every initial distribution, we determine whether the conditional law converges to a QSD and identify that QSD whenever it does. The necessary and sufficient criteria are formulated in terms of the tail probabilities and moments of the initial law.
ER -