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System control and rough paths

Author: T J Lyons; Zhongmin Qian
Publisher: Oxford : Clarendon Press ; New York : Oxford University Press, 2002.
Series: Oxford mathematical monographs.; Oxford science publications.
Edition/Format:   Print book : EnglishView all editions and formats
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.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: T J Lyons; Zhongmin Qian
ISBN: 0198506481 9780198506485
OCLC Number: 51483643
Description: x, 216 pages ; 24 cm.
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.
Series Title: Oxford mathematical monographs.; Oxford science publications.
Responsibility: Terry Lyons and Zhongmin Qian.
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Abstract:

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.  Read more...

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This book is very interesting and provides a theoretical platform for further developments. * Zentralblatt MATH *

 
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