Ergodic properties of subcritical multitype Galton-Watson processes
G\'abor Sz\H{u}cs
TL;DR
This paper proves the existence of stationary distributions for subcritical multitype Galton-Watson processes without restrictions on the offspring mean matrix, and explores additional properties of these distributions.
Contribution
It establishes the existence of stationary distributions under minimal conditions and analyzes their properties, advancing understanding of multitype Galton-Watson processes.
Findings
Stationary distributions exist without conditions on the mean matrix.
Additional properties of these distributions are characterized.
Results apply to subcritical multitype Galton-Watson processes.
Abstract
We show the existance of the stationary distributions of subcritical multitype Galton-Watson processes without any conditions on the mean matrix of the offspring distributions. Some additional properties of the stationary distribution are also proven.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Stochastic processes and financial applications