Scaling Limits of Controlled Branching Processes
Jiawei Liu
TL;DR
This paper studies the asymptotic behavior of a specific class of controlled branching processes, establishing conditions under which they converge to continuous processes with dependent immigration.
Contribution
It introduces a simple set of sufficient conditions for the weak convergence of controlled branching processes to continuous branching processes with dependent immigration.
Findings
Established weak convergence under specified conditions
Identified continuous limits with dependent immigration
Provided a framework for analyzing controlled branching processes
Abstract
In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes with dependent immigration.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Cellular Automata and Applications