Rate of convergence of uniform transport processes to Brownian sheet

TL;DR

This paper establishes the rate at which a family of processes, constructed from independent Poisson processes, converges uniformly to the Brownian sheet, providing quantitative convergence insights.

Contribution

It provides the first explicit rate of convergence for processes constructed from Poisson processes towards the Brownian sheet.

Findings

Quantitative rate of convergence derived

Processes from Poisson processes approach Brownian sheet almost surely

Uniform convergence rate established

Abstract

In a previous paper we have constructed a family of processes, starting from a set of independent standard Poisson processes, that has realizations that converge almost surely to the Brownian sheet, uniformly in the unit square. Now, a rate of convergence from these processes to Brownian sheet is given.