System Control and Rough Paths

This book describes a completely novel mathematical development which has already influenced probability theory and has potential for application to engineering and to areas of pure mathematics. Intended for probabilists mathematicians and engineers with a mathematical background from graduate level onwards this book develops the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli. Attention is focussed on an analysis of the relationship between the stimulus and the short to medium term evolution of a receiver. The core result of the book is a continuity theorum that proves that the response of the system depends continuously on these nilpotent elements.