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Multiple Wiener Ito Integrals
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Book Synopsis Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications by : Christian Houdre
Download or read book Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications written by Christian Houdre and published by CRC Press. This book was released on 1994-04-05 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of chaos expansions and multiple Wiener-Ito integrals has become a field of considerable interest in applied and theoretical areas of probability, stochastic processes, mathematical physics, and statistics. Divided into four parts, this book features a wide selection of surveys and recent developments on these subjects. Part 1 introduces the concepts, techniques, and applications of multiple Wiener-Ito and related integrals. The second part includes papers on chaos random variables appearing in many limiting theorems. Part 3 is devoted to mixing, zero-one laws, and path continuity properties of chaos processes. The final part presents several applications to stochastic analysis.
Book Synopsis Multiple Wiener-Ito Integrals by : P. Major
Download or read book Multiple Wiener-Ito Integrals written by P. Major and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Wiener-Ito Integrals by : Springer
Download or read book Multiple Wiener-Ito Integrals written by Springer and published by . This book was released on 2014-01-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Wiener-Itô Integrals by : Péter Major
Download or read book Multiple Wiener-Itô Integrals written by Péter Major and published by Springer. This book was released on 2013-12-02 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener–Itô integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced that enables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revised version of a previous volume written with the goal of giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results; it was written to give a better insight to the old ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carrying out heuristic arguments.
Book Synopsis Multiple Wiener-Ito Integrals by : Springer
Download or read book Multiple Wiener-Ito Integrals written by Springer and published by . This book was released on 2013-12-31 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extension of Ito's Calculus Via Malliavin Calculus by : A. S. Ustunel
Download or read book Extension of Ito's Calculus Via Malliavin Calculus written by A. S. Ustunel and published by . This book was released on 1985 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to the development of the Ito's calculus for a class of functionals defined on the Wiener space which are more general objects than semimartingales. In doing this, we begin by an extension if the Ito formula for finite dimensional hypoelliptic Ito processes to the tempered distributions. Watanabe has defined the composition of a tempered distribution by a hypoelliptic Wiener functional with the help of the Malliavin Calculus. Here we go a little further and give an Ito formula by using the same method. Let us note that when the Ito process is the standard Wiener process, the Ito formula has already been extended to the tempered distributions with the use of the Hida calculus; we give here a different approach which works for more general processes than the standard Wiener process. In the extended Ito formula, the Lebesgue integral part can be interpreted as a Bochner integral in some Sobolev space on the Weiner space and the notations; however the remaining part is not an ordinary stochastic integral, despite the fact that it corresponds to a functional in some Sobolev space on the Wiener space. This situation suggests an extension of the Ito stochastic integral to the objects which are not necessarily stochastic processes.
Book Synopsis Multiple Wiener Integrals and Nonlinear Functionals of a Nuclear Space Valued Wiener Process by : Víctor Pérez Abreu
Download or read book Multiple Wiener Integrals and Nonlinear Functionals of a Nuclear Space Valued Wiener Process written by Víctor Pérez Abreu and published by . This book was released on 1985 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let phi be the dual of a Countably Hilbert nuclear space and W sub t be a phi-Wiener process. This work constructs stochastic integrals and multiple Wiener integrals of operator valued processes with respect to W sub t. The Wiener decomposition of the space of phi-valued nonlinear functionals of W sub t is established. Also obtained are multiple stochastic integral expansions and representations of phi-valued nonlinear functionals of W sub t operator valued stochastic integrals of Ito type. (Author).
Book Synopsis Introduction to Stochastic Integration by : Hui-Hsiung Kuo
Download or read book Introduction to Stochastic Integration written by Hui-Hsiung Kuo and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews: "Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY
Book Synopsis Quantum Probability for Probabilists by : Paul-Andre Meyer
Download or read book Quantum Probability for Probabilists written by Paul-Andre Meyer and published by Springer. This book was released on 2013-11-11 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability" , the main topic is "Quantum Stochastic Calculus" , a field which has recently got official recognition as 81825 in the Math.
Book Synopsis The Multiple Stochastic Integral by : David Douglas Engel
Download or read book The Multiple Stochastic Integral written by David Douglas Engel and published by American Mathematical Soc.. This book was released on 1982 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author establishes a relation between the theory of multiple stochastic integration and the theory of Banach space valued measures.
Book Synopsis The Malliavin Calculus and Related Topics by : David Nualart
Download or read book The Malliavin Calculus and Related Topics written by David Nualart and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [176]. Later these notes were completed and improved in two courses on Malliavin cal culus given at the University of California at Irvine in 1986 and at Ecole Polytechnique Federale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was de veloped from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Prob ability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions.
Book Synopsis Stochastic Filtering Theory by : G. Kallianpur
Download or read book Stochastic Filtering Theory written by G. Kallianpur and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests at the time and the needs of the students taking the course. Initially the lectures were written up for publication in the Lecture Notes series. How ever, when I accepted Professor A. V. Balakrishnan's invitation to publish them in the Springer series on Applications of Mathematics it became necessary to alter the informal and often abridged style of the notes and to rewrite or expand much of the original manuscript so as to make the book as self-contained as possible. Even so, no attempt has been made to write a comprehensive treatise on filtering theory, and the book still follows the original plan of the lectures. While this book was in preparation, the two-volume English translation of the work by R. S. Liptser and A. N. Shiryaev has appeared in this series. The first volume and the present book have the same approach to the sub ject, viz. that of martingale theory. Liptser and Shiryaev go into greater detail in the discussion of statistical applications and also consider inter polation and extrapolation as well as filtering.
Book Synopsis Analysis On Gaussian Spaces by : Yaozhong Hu
Download or read book Analysis On Gaussian Spaces written by Yaozhong Hu and published by World Scientific. This book was released on 2016-08-30 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors.'Mathematical Reviews ClippingsAnalysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the Gaussian measure, which has been unified under the terminology of 'abstract Wiener space'.Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the Gaussian space itself such as the Brunn-Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the Gaussian space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood-Paley-Stein-Meyer theory are given in details.This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood-Paley-Stein-Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.
Book Synopsis Stochastic Analysis And Applications: Proceedings Of The Fifth Gregynog Symposium by : Ian M Davies
Download or read book Stochastic Analysis And Applications: Proceedings Of The Fifth Gregynog Symposium written by Ian M Davies and published by World Scientific. This book was released on 1996-03-20 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers which were presented at a meeting entitled “Stochastic Analysis and Applications“ held at Gregynog Hall, Powys, from the 9th — 14th July 1995. The meeting consisted of a mixture of plenary/review talks and special interest sessions covering most of the current areas of activity in stochastic analysis. The meeting was jointly organized by the Department of Mathematics, University of Wales Swansea and the Mathematics Institute, University of Warwick in connection with the Stochastic Analysis year of activity. The papers contained herein are accessible to workers in the field of stochastic analysis and give a good coverage of topics of current interest in the research community.
Book Synopsis Tai Shu, Chi Ho, Fen Hsi Yen Tʻao Hui by :
Download or read book Tai Shu, Chi Ho, Fen Hsi Yen Tʻao Hui written by and published by . This book was released on 1988 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Stochastic Differential Equations by : Peter E. Kloeden
Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2011-06-15 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Book Synopsis Gaussian Measures by : Vladimir I. Bogachev
Download or read book Gaussian Measures written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2015-01-26 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.
