Infinitely many Brownian globules with Brownian radii

TL;DR

This paper models an infinite system of spherical globules with random, time-varying radii undergoing Brownian motion in three-dimensional space, establishing existence, uniqueness, and reversible measures for the system.

Contribution

It introduces a novel infinite-dimensional stochastic differential equation framework for globules with random radii, proving well-posedness and identifying reversible measures.

Findings

Existence and uniqueness of strong solutions for the system

Identification of a class of reversible measures

Framework for globules with stochastic radii in infinite dimensions

Abstract

We consider an infinite system of non overlapping globules undergoing Brownian motions in R^3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional Stochastic Differential Equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.