Domain of attraction of the fixed points of Branching Brownian motion

TL;DR

This paper characterizes the domain of attraction of fixed points in branching Brownian motion with critical drift, establishing a Markov process framework and exploring various applications of this classification.

Contribution

It provides a complete classification of the domain of attraction for fixed points of BBM with critical drift, including a new metric space and Markov process properties.

Findings

BBM with critical drift is a well-defined Markov process

The process satisfies the Feller property

Applications of the classification are demonstrated

Abstract

We give a complete characterisation of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a suitable metric space of locally finite point measures on which we prove 1) that the BBM with critical drift is a well-defined Markov process and 2) that it satisfies the Feller property. Several applications of this characterisation are given.