The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics

Author : Nicolai Victorovich Norin
Publisher : World Scientific
Page : 280 pages
File Size : 40,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9810225687

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The Extended Stochastic Integral in Linear Spaces with Differentiable Measures and Related Topics by Nicolai Victorovich Norin Pdf

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.

Author : Vladimir Igorevich Bogachev
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 40,7 Mb
Release : 2010-07-21
Category : Mathematics
ISBN : 9780821849934

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Differentiable Measures and the Malliavin Calculus by Vladimir Igorevich Bogachev Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 1770 pages
File Size : 42,8 Mb
Release : 2004
Category : Mathematics
ISBN : UVA:X006180633

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 536 pages
File Size : 48,8 Mb
Release : 1999
Category : Mathematics
ISBN : UOM:39015049390423

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Doklady by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 2312 pages
File Size : 52,5 Mb
Release : 1997
Category : American literature
ISBN : UOM:39015058373732

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The Cumulative Book Index by Anonim Pdf

A world list of books in the English language.

Author : Anonim
Publisher : Unknown
Page : 1294 pages
File Size : 53,9 Mb
Release : 1998
Category : English imprints
ISBN : UOM:39015046780444

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International Books in Print by Anonim Pdf

Author : G K HALL,G. K. Hall and Co. Staff
Publisher : Macmillan Reference USA
Page : 672 pages
File Size : 48,8 Mb
Release : 1997-07
Category : Reference
ISBN : 078381755X

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Bibliographic Guide to East Asian Studies 1996 by G K HALL,G. K. Hall and Co. Staff Pdf

Author : Anonim
Publisher : Unknown
Page : 760 pages
File Size : 54,9 Mb
Release : 1990
Category : Mathematicians
ISBN : UOM:39015039029916

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Russian Mathematical Surveys by Anonim Pdf

Author : David Nualart
Publisher : Springer
Page : 266 pages
File Size : 42,8 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780387944326

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The Malliavin Calculus and Related Topics by David Nualart Pdf

The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space. Originally, it was developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems. This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus. The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hormander's theorem. Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions. Readers are assumed to have a firm grounding in probability as might be gained from a graduate course in the subject. Exercises at the end of each chapter help to reinforce a reader's understanding and to extend some of the ideas covered, and each chapter ends with a discussion of further directions that research has taken.

Author : Fima C. Klebaner
Publisher : Imperial College Press
Page : 431 pages
File Size : 48,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945557

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Introduction to Stochastic Calculus with Applications by Fima C. Klebaner Pdf

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Author : Anonim
Publisher : Unknown
Page : 1090 pages
File Size : 43,9 Mb
Release : 1989
Category : Statistics
ISBN : MINN:31951P000229441

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Statistical Theory and Method Abstracts by Anonim Pdf

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 50,9 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author : Geoffrey Knight
Publisher : Unknown
Page : 558 pages
File Size : 42,9 Mb
Release : 1969
Category : Computer science
ISBN : STANFORD:36105031364594

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Computer Mathematics, Series II by Geoffrey Knight Pdf

General numerical and symbolic analysis; Elementary algebra; Calculus; Difference, differential and integral equations; Abstracts mathematics; Probability and statistics; Optimization mathematical programming: operations research; Mathematical communication theory: information theory; Mathematical systems and control theory; Mathematical logic and switching theory: automata.

Author : Anonim
Publisher : Unknown
Page : 232 pages
File Size : 44,7 Mb
Release : 1970
Category : Science
ISBN : UIUC:30112101038153

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U.S. Government Research & Development Reports by Anonim Pdf

Author : Geoffrey Knight
Publisher : Unknown
Page : 552 pages
File Size : 41,9 Mb
Release : 1968
Category : Electronic data processing
ISBN : UOM:39015002092289

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Cumulative Computer Abstracts by Geoffrey Knight Pdf