On the splitting-up method for rough (partial) differential equations

TL;DR

This paper introduces a splitting method for solving systems of rough partial differential equations and rough differential equations, with applications in control theory and nonlinear filtering.

Contribution

It presents a novel splitting approach tailored for systems driven by rough paths, extending existing methods to nonlinear PDEs with rough noise.

Findings

Effective splitting scheme for rough PDEs demonstrated

Applications to stochastic PDEs in control and filtering shown

Method improves computational handling of rough noise in PDEs

Abstract

This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to stochastic partial differential equations arising in control theory and nonlinear filtering are given.