Title System control and rough paths / Terry Lyons and Zhongmin Qian

Published Oxford : Clarendon Press ; New York : Oxford University Press, 2002

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Description 1 online resource (x, 216 pages) Series Oxford mathematical monographs Oxford science publications Oxford mathematical monographs. Oxford science publications. Contents Controlled systems -- Vector systems -- Iterated integral expansions -- Mathematics of rough paths -- Lipschitz paths -- Integration theory -- Equations driven by Lipschitz paths -- Existence of solutions -- Uniqueness -- Existence of solutions revisited -- Continuity of the Ito map -- Rough paths -- Basic definitions and properties -- The binomial inequality -- Several basic results -- Almost rough paths -- Spaces of rough paths -- Variation distances and variation topology -- Young's integration theory -- Elementary operations on rough paths -- Brownian rough paths -- Control variation distances -- Dyadic polygonal approximations -- Holder's condition -- Processes with long-time memory -- Gaussian processes -- Wiener processes in Banach spaces -- Gaussian analysis -- Wiener processes as geometric rough paths -- Path integration along rough paths -- Lipschitz one-forms -- Integration theory: degree two -- Lipschitz continuity of integration -- Ito's formula and stochastic integration -- Ito's formula -- Stochastic integration -- Integration against geometric rough paths -- Banach tensor products -- Differentiation, Taylor's theorem -- Universal limit theorem -- Ito maps: rough paths with 2 [less than or equal] p [less than sign] 3 -- The Picard iteration -- Basic estimates -- Lipschitz continuity -- Uniqueness -- Continuity theorem -- Flows of diffeomorphisms -- The Ito map: geometric rough paths -- Vector fields and flow equations -- Smoothness of Ito maps -- Ito's vector fields -- Flows of Ito vector fields Summary This work 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: the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli Bibliography Includes bibliographical references (pages 205-213) and index Notes Print version record Subject Stochastic processes. Stochastic Processes MATHEMATICS -- Probability & Statistics -- Stochastic Processes. Stochastic processes Systeemtheorie. Controleleer. Stochastische processen. Form Electronic book Author Qian, Zhongmin, author. ISBN 9780191523120 0191523127 9780191709395 0191709395

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