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System Control and Rough Paths

Terry Lyons and Zhongmin Qian


Systems evolve and interact, and when they do this in a continuous way, differential equations can be used to provide accurate mathematical models for the interaction or reaction of the controlled system to external stimuli or forcing. If the forcing is not smooth on normal scales, one cannot use classical calculus. The theory of rough paths provides a rigorous mathematical extension of Newtonian calculus, allowing one to model the responses of systems subject to more wildly oscillating or ‘rough’ stimuli. This book defines rough paths as the completion of the piecewise smooth paths under a p- ... More

Keywords: Chen iterated integral, controlled differential equation, stochastic differential equation, infinite dimensional stochastic differential equation, Itô functional

Bibliographic Information

Print publication date: 2002 Print ISBN-13: 9780198506485
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780198506485.001.0001


Affiliations are at time of print publication.

Terry Lyons, author
Wallis Professor of Mathematics, University of Oxford and St Anne's College

Zhongmin Qian, author
Chargé de recherche, CNRS (France) and University Paul-Sabatier