Coagulation dynamics under environmental noise: scaling limit to SPDE

TL;DR

This paper demonstrates that a system of interacting diffusions with environmental noise and coagulation converges to a well-defined SPDE, establishing existence, uniqueness, and regularity of the limiting equations.

Contribution

It introduces a rigorous convergence result from particle systems to SPDEs with nonlinear coagulation dynamics under environmental noise.

Findings

Convergence of particle system to SPDE with coagulation.

Proof of existence and uniqueness for the SPDE.

Regularity results for the solutions of the SPDE.

Abstract

We prove that a system of locally interacting diffusions carrying discrete masses, subject to an environmental noise and undergoing mass coagulation, converges to a system of Stochastic Partial Differential Equations (SPDEs) with Smoluchowski-type nonlinearity. Existence, uniqueness and regularity of the SPDEs are also proven.