New directions in the applications of rough path theory

Rough path theory is an abstract mathematical tool-set that allows the modelling This article provides a concise overview of and analysis of evolving systems across a some of the recent advances in the application broad spectrum of use cases. It extends of rough path theory to machine Newton's and Itô's calculus to model the learning. Controlled differential equations interactions of complex and messy data (CDEs) are discussed as the key mathematical streams. It has been influential within model to describe the interaction mathematics, in particular in stochastic of a stream with a physical control system.