An Introduction To The Geometry Of Stochastic Flows
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An Introduction To The Geometry Of Stochastic Flows
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Author : Fabrice Baudoin
language : en
Publisher: World Scientific
Release Date : 2004-11-10
An Introduction To The Geometry Of Stochastic Flows written by Fabrice Baudoin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-10 with Mathematics categories.
This book aims to provide a self-contained introduction to the local geometry of the stochastic flows. It studies the hypoelliptic operators, which are written in Hörmander's form, by using the connection between stochastic flows and partial differential equations.The book stresses the author's view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry, and its main tools are introduced throughout the text./a
An Introduction To The Geometry Of Stochastic Flows
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Author : Fabrice Baudoin
language : en
Publisher: World Scientific
Release Date : 2004
An Introduction To The Geometry Of Stochastic Flows written by Fabrice Baudoin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book aims to provide a self-contained introduction to the local geometry of the stochastic flows associated with stochastic differential equations. It stresses the view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry whose main tools are introduced throughout the text. By using the connection between stochastic flows and partial differential equations, we apply this point of view of the study of hypoelliptic operators written in Hormander's form.
On The Geometry Of Diffusion Operators And Stochastic Flows
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Author : K.D. Elworthy
language : en
Publisher: Springer
Release Date : 2007-01-05
On The Geometry Of Diffusion Operators And Stochastic Flows written by K.D. Elworthy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Stochastic Flows And Stochastic Differential Equations
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Author : Hiroshi Kunita
language : en
Publisher: Cambridge University Press
Release Date : 1990
Stochastic Flows And Stochastic Differential Equations written by Hiroshi Kunita and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows.The classical theory was initiated by K. Itô and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby Itô's theory as a special case. The book can be used with advanced courses on probability theory or for self-study.
Measure Valued Processes And Stochastic Flows
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Author : Andrey A. Dorogovtsev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-06
Measure Valued Processes And Stochastic Flows written by Andrey A. Dorogovtsev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Mathematics categories.
This book discusses the systems of interacting particles evolving in the random media. The focus is on the study of both the finite subsystems motion and the flow, describing motion of all particles in the space. The integral characteristics of the system and mass distribution are also covered and results are illustrated with examples from turbulence theory, synchronization and DNA evolution.
Stochastic Geometric Analysis With Applications
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Author : Ovidiu Calin
language : en
Publisher: World Scientific
Release Date : 2023-11-21
Stochastic Geometric Analysis With Applications written by Ovidiu Calin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-21 with Mathematics categories.
This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.
S Minaire De Probabilit S Xlii
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Author : Catherine Donati-Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-29
S Minaire De Probabilit S Xlii written by Catherine Donati-Martin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-29 with Mathematics categories.
The tradition of specialized courses in the Séminaires de Probabilités is continued with A. Lejay's Another introduction to rough paths. Other topics from this 42nd volume range from the interface between analysis and probability to special processes, Lévy processes and Lévy systems, branching, penalization, representation of Gaussian processes, filtrations and quantum probability.
A Course On Rough Paths
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Author : Peter K. Friz
language : en
Publisher: Springer Nature
Release Date : 2020-05-27
A Course On Rough Paths written by Peter K. Friz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-27 with Mathematics categories.
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Stochastic Differential Equations On Manifolds
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Author : K. D. Elworthy
language : en
Publisher: Cambridge University Press
Release Date : 1982
Stochastic Differential Equations On Manifolds written by K. D. Elworthy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Manifolds (Mathematics). categories.
The aims of this book, originally published in 1982, are to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory. The author has included two appendices which summarise the manifold theory and differential geometry needed to follow the development; coordinate-free notation is used throughout. Moreover, the stochiastic integrals used are those which can be obtained from limits of the Riemann sums, thereby avoiding much of the technicalities of the general theory of processes and allowing the reader to get a quick grasp of the fundamental ideas of stochastic integration as they are needed for a variety of applications.
An Introduction To Rings And Modules
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Author : A. J. Berrick
language : en
Publisher: Cambridge University Press
Release Date : 2000-05
An Introduction To Rings And Modules written by A. J. Berrick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05 with Mathematics categories.
This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.