The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics
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The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics
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Author : Nicolai Victorovich Norin
language : en
Publisher: World Scientific
Release Date : 1996-08-30
The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics written by Nicolai Victorovich Norin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-30 with Mathematics categories.
This volume discusses the extended stochastic integral (ESI) (or Skorokhod-Hitsuda Integral) and its relation to the logarithmic derivative of differentiable measure along the vector or operator field. In addition, the theory of surface measures and the theory of heat potentials in infinite-dimensional spaces are discussed. These theories are closely related to ESI.It starts with an account of classic stochastic analysis in the Wiener spaces; and then discusses in detail the ESI for the Wiener measure including properties of this integral understood as a process. Moreover, the ESI with a nonrandom kernel is investigated.Some chapters are devoted to the definition and the investigation of properties of the ESI for Gaussian and differentiable measures.Surface measures in Banach spaces and heat potentials theory in Hilbert space are also discussed.
Differentiable Measures And The Malliavin Calculus
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Author : Vladimir Igorevich Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-07-21
Differentiable Measures And The Malliavin Calculus written by Vladimir Igorevich Bogachev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-21 with Mathematics categories.
This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
The Non Uniform Riemann Approach To Stochastic Integration
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Author : Varayu Boonpogkrong
language : en
Publisher: World Scientific
Release Date : 2024-09-17
The Non Uniform Riemann Approach To Stochastic Integration written by Varayu Boonpogkrong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-17 with Mathematics categories.
This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.
Doklady
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Author :
language : en
Publisher:
Release Date : 1999
Doklady written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Stochastic Partial Differential Equations
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Author : Sergey V. Lototsky
language : en
Publisher: Springer
Release Date : 2017-07-06
Stochastic Partial Differential Equations written by Sergey V. Lototsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.
Research In Progress
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Author :
language : en
Publisher:
Release Date : 1971
Research In Progress written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Military research categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1998
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Estimation And Control Problems For Stochastic Partial Differential Equations
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Author : Pavel S. Knopov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-17
Estimation And Control Problems For Stochastic Partial Differential Equations written by Pavel S. Knopov 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 2013-09-17 with Mathematics categories.
Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered. More generally, this book is intended for scientists, graduate, and post-graduates specializing in probability theory and mathematical statistics. The models presented describe many processes in turbulence theory, fluid mechanics, hydrology, astronomy, and meteorology, and are widely used in pattern recognition theory and parameter identification of stochastic systems. Therefore, this book may also be useful to applied mathematicians who use probability and statistical methods in the selection of useful signals subject to noise, hypothesis distinguishing, distributed parameter systems optimal control, and more. Material presented in this monograph can be used for education courses on the estimation and control theory of random fields.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2012-12-06 with Mathematics categories.
This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Loeb Measures In Practice Recent Advances
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Author : Nigel Cutland
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-12-12
Loeb Measures In Practice Recent Advances written by Nigel Cutland 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 2000-12-12 with Business & Economics categories.
This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.