system control and rough paths oxford mathematical monographs

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System Control And Rough Paths

Author : Terry Lyons
ISBN : 0198506481
Genre : Mathematics
File Size : 43. 30 MB
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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 Ito theory but also allowing new 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'.

A Course On Rough Paths

Author : Peter K. Friz
ISBN : 9783319083322
Genre : Mathematics
File Size : 87. 80 MB
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Lyons’ rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension – the theory of regularity structures – and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.

Differential Equations Driven By Rough Paths

Author : Terry J. Lyons
ISBN : 9783540712855
Genre : Mathematics
File Size : 41. 83 MB
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Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory. The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths.

S Minaire De Probabilit S Xlvi

Author : Catherine Donati-Martin
ISBN : 9783319119700
Genre : Mathematics
File Size : 47. 9 MB
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Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.

S Minaire De Probabilit S

Author : J. Azéma
ISBN : UOM:39015081661442
Genre : Mathematics
File Size : 45. 67 MB
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Contents of 1-14 (1966/67-1978/79) in v. 15 (1979/80)

Annales Scientifiques De L Cole Normale Sup Rieure

Author :
ISBN : UOM:39015068700510
Genre : Science
File Size : 64. 54 MB
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The Universality Of The Radon Transform

Author : Leon Ehrenpreis
ISBN : 9780198509783
Genre : Mathematics
File Size : 88. 53 MB
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Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging. The first part of the book discusses parametricand nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincare, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding.This is the latest title in the Oxford Mathematical Monographs, which includes texts and monographs covering many topics of current research interest in pure and applied mathematics. Other titles include: Carbone and Semmes: A graphic apology for symmetry and implicitness; Higson and Roe: Analytic K-Homology; Iwaniec and Martin: Geometric Function Theory and Nonlinear Analysis; Lyons and Qian: System Control and Rough Paths. Also new in paperback Johnson and Lapidus: The Feynman Integral andFeynman's Operational Calculus; Donaldson and Kronheimer: The geometry of four-manifolds.

Annales De L I H P

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ISBN : UOM:39015058994297
Genre : Probabilities
File Size : 24. 22 MB
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Revista Matem Tica Iberoamericana

Author :
ISBN : UCSD:31822036059848
Genre : Mathematics
File Size : 75. 55 MB
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Numerical Analysis And Applied Mathematics

Author : Theodore E. Simos
ISBN : 073540447X
Genre : Science
File Size : 79. 76 MB
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This volume contains peer-reviewed papers presented at the International Conference on Numerical Analysis and Applied Mathematics 2007, ICNAAM-2007. This conference brought together leading scientists of the international Numerical and Applied Mathematics community. More than 350 papers were submitted to be considered for presentation at ICNAAM-2007. From these submissions, 189 papers were selected after an international peer review by at least two independent reviewers.

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