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.

About the Author

Terry Lyons is Wallis Professor of Mathematics, University of Oxford and St Anne's College. Zhongmin Qian is at Charg� de recherche, CNRS (France) and University Paul-Sabatier.

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