One Brownian Stochastic Flow

TL;DR

This paper studies the weak limits of measure-valued processes formed by interacting Brownian particles, resulting in the derivation of the Arrattia flow as a limiting stochastic flow.

Contribution

It introduces a new analysis of measure-valued processes and establishes the Arrattia flow as a novel limiting stochastic flow for interacting Brownian particles.

Findings

Weak limits of measure-valued processes are characterized.

Arrattia flow is derived as the limiting stochastic flow.

Provides a new framework for analyzing interacting Brownian particles.

Abstract

The weak limits of the measure-valued processes organized as a mass carried by the interacting Brownian particles are described. As a limiting flow the Arrattia flow is obtained.