Optimisation-based representations for branching processes

TL;DR

This paper introduces optimization-based representations for functionals of branching processes, enabling easy bounds and applications like calculating the speed of the right-most particle in a branching Levy process.

Contribution

It provides novel dual optimization representations for branching process functionals, facilitating bounds and practical calculations.

Findings

Derived non-asymptotic Trotter product formula.

Calculated the speed of the right-most particle in a branching Levy process.

Established dual maximization and minimization representations.

Abstract

It is shown that a certain functional of a branching process has representations in terms of both a maximisation problem and a minimisation problem. A consequence of these representation is that upper and lower bounds on the functional can be found easily, yielding a non-asymptotic Trotter product formula. As an application, the speed of the right-most particle of a branching Levy process is calculated.