SPDEs on narrow domains and on graphs: an asymptotic approach

TL;DR

This paper introduces a novel approach to deriving stochastic partial differential equations on graphs as limits of equations in narrow channels, pioneering the study of SPDEs on graph structures.

Contribution

It presents the first study of SPDEs on graphs, establishing a rigorous asymptotic connection from narrow domain equations to graph-based equations.

Findings

SPDEs on graphs can be obtained as limits of narrow channel SPDEs

First rigorous analysis of SPDEs on graph structures

Methodology bridges PDEs in narrow domains and graph-based models

Abstract

We introduce here a class of stochastic partial differential equations defined on a graph and we show how they are obtained as the limit of suitable stochastic partial equations defined in a narrow channel, as the width of the channel goes to zero. To our knowledge, this is the first time an SPDE on a graph is studied.