Articles liés à System Control and Rough Paths
Synopsis
Book by Lyons Terry Qian Zhongmin
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Présentation de l'éditeur
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 (or control) and the short to medium term evolution of a receiver (the response of the system). A rapidly fluctuation stimuli can be likened to a huge dataset; and a basic question is how best to reduce this dataset so as to capture the critical information and little else. An essential component problem involves identifying the point at which two different stimuli produce essentially the same response from the class of receivers. (When do two stereo sounds sound the same?). This is an essentially non-linear problem that requires novel mathematics. At one level, this book focuses on systems responding to such rough external stimuli, and demonstrates that the natural reduction approximates the stimuli as a sequence of nilpotent elements. The core result of the book is a continuity theorem that proves that the response of the system depends continuously on these nilpotent elements. A key mathematical aspect of the book is the notion of a rough path, based on combining the notion of p-variation of Wiener with the iterated integral expansions of paths introduced by K. T. Chen. The continuity theorem for these rough paths gives a new way to construct solutions to stochastic differential equations, providing a fresh approach to the Itô theory but also allowing new kinds of noisy perturbations (such as Fractional Brownian Motions) that cannot be discussed in the standard Itô approach. It also provides some interesting concrete examples of 'continuous free groups'.
Revue de presse
This book is very interesting and provides a theoretical platform for further developments. (Zentralblatt MATH)
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurOxford University Press
- Date d'édition2002
- ISBN 10 0198506481
- ISBN 13 9780198506485
- ReliureRelié
- Langueanglais
- Nombre de pages228
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System Control and Rough Paths (Hardcover)
Edité par
Oxford University Press, Oxford, 2002
ISBN 10 : 0198506481
ISBN 13 : 9780198506485
Neuf
Couverture rigide
Vendeur : AussieBookSeller, Truganina, VIC, Australie
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Hardcover. Etat : new. Hardcover. 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 onan analysis of the relationship between the stimulus (or control) and the short to medium term evolution of a receiver (the response of the system).A rapidly fluctuation stimulican be likened to a huge dataset; and a basic question is how best to reduce this dataset so as to capture the critical information and little else. An essential component problem involves identifying the point at which two different stimuli produce essentially the same response from the class of receivers. (When do two stereo sounds sound the same?). This is an essentially non-linear problem that requires novel mathematics.At one level, this book focuses on systemsresponding to such rough external stimuli, and demonstrates that the natural reduction approximates the stimuli as a sequence of nilpotent elements. The core result of the book is a continuity theorem thatproves that the response of the system depends continuously on these nilpotent elements.A key mathematical aspect of the book is the notion of a rough path, based on combining the notion of p-variation of Wiener with the iterated integral expansions of paths introduced by K. T. Chen. The continuity theorem for these rough paths gives a new way to construct solutions to stochastic differential equations, providing a fresh approach to the Ito theory but also allowingnew kinds of noisy perturbations (such as Fractional Brownian Motions) that cannot be discussed in the standard Ito approach. It also provides some interesting concrete examples of 'continuous freegroups'. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. N° de réf. du vendeur 9780198506485
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System Control and Rough Paths (Oxford Mathematical Monographs)
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System Control and Rough Paths (Oxford Mathematical Monographs)
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System Control and Rough Paths (Hardcover)
Edité par
Oxford University Press, Oxford, 2002
ISBN 10 : 0198506481
ISBN 13 : 9780198506485
Neuf
Couverture rigide
Vendeur : CitiRetail, Stevenage, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
Hardcover. Etat : new. Hardcover. 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 onan analysis of the relationship between the stimulus (or control) and the short to medium term evolution of a receiver (the response of the system).A rapidly fluctuation stimulican be likened to a huge dataset; and a basic question is how best to reduce this dataset so as to capture the critical information and little else. An essential component problem involves identifying the point at which two different stimuli produce essentially the same response from the class of receivers. (When do two stereo sounds sound the same?). This is an essentially non-linear problem that requires novel mathematics.At one level, this book focuses on systemsresponding to such rough external stimuli, and demonstrates that the natural reduction approximates the stimuli as a sequence of nilpotent elements. The core result of the book is a continuity theorem thatproves that the response of the system depends continuously on these nilpotent elements.A key mathematical aspect of the book is the notion of a rough path, based on combining the notion of p-variation of Wiener with the iterated integral expansions of paths introduced by K. T. Chen. The continuity theorem for these rough paths gives a new way to construct solutions to stochastic differential equations, providing a fresh approach to the Ito theory but also allowingnew kinds of noisy perturbations (such as Fractional Brownian Motions) that cannot be discussed in the standard Ito approach. It also provides some interesting concrete examples of 'continuous freegroups'. 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. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de réf. du vendeur 9780198506485
Quantité disponible : 1 disponible(s)
Image d'archives
System Control and Rough Paths (Hardcover)
Edité par
Oxford University Press, Oxford, 2002
ISBN 10 : 0198506481
ISBN 13 : 9780198506485
Neuf
Couverture rigide
Vendeur : Grand Eagle Retail, Fairfield, OH, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Hardcover. Etat : new. Hardcover. 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 onan analysis of the relationship between the stimulus (or control) and the short to medium term evolution of a receiver (the response of the system).A rapidly fluctuation stimulican be likened to a huge dataset; and a basic question is how best to reduce this dataset so as to capture the critical information and little else. An essential component problem involves identifying the point at which two different stimuli produce essentially the same response from the class of receivers. (When do two stereo sounds sound the same?). This is an essentially non-linear problem that requires novel mathematics.At one level, this book focuses on systemsresponding to such rough external stimuli, and demonstrates that the natural reduction approximates the stimuli as a sequence of nilpotent elements. The core result of the book is a continuity theorem thatproves that the response of the system depends continuously on these nilpotent elements.A key mathematical aspect of the book is the notion of a rough path, based on combining the notion of p-variation of Wiener with the iterated integral expansions of paths introduced by K. T. Chen. The continuity theorem for these rough paths gives a new way to construct solutions to stochastic differential equations, providing a fresh approach to the Ito theory but also allowingnew kinds of noisy perturbations (such as Fractional Brownian Motions) that cannot be discussed in the standard Ito approach. It also provides some interesting concrete examples of 'continuous freegroups'. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9780198506485
Quantité disponible : 1 disponible(s)
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System Control and Rough Paths
Edité par
Clarendon Press, 2003
ISBN 10 : 0198506481
ISBN 13 : 9780198506485
Ancien ou d'occasion
Couverture rigide
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
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