Stochastic Integration And Generalized Martingales
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Stochastic Integration And Generalized Martingales
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Author : A. U. Kussmaul
language : en
Publisher: Pitman Publishing
Release Date : 1977
Stochastic Integration And Generalized Martingales written by A. U. Kussmaul and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Stochastic Integration And Generalized Martingales
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Author : Alfred Kussmaul
language : en
Publisher:
Release Date : 1977
Stochastic Integration And Generalized Martingales written by Alfred Kussmaul and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Martingales (Mathematics) categories.
Stochastic Processes General Theory
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Author : Malempati M. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Stochastic Processes General Theory written by Malempati M. Rao 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 2013-03-14 with Mathematics categories.
Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.
Stochastic Integration
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Author : Michel Metivier
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Stochastic Integration written by Michel Metivier and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.
Stochastic Integration And Differential Equations
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Author : Philip Protter
language : en
Publisher: Springer
Release Date : 2013-12-21
Stochastic Integration And Differential Equations written by Philip Protter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
Brownian Motion Martingales And Stochastic Calculus
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Author : Jean-François Le Gall
language : en
Publisher: Springer
Release Date : 2016-04-28
Brownian Motion Martingales And Stochastic Calculus written by Jean-François Le Gall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Mathematics categories.
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
Martingales And Stochastic Analysis
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Author : James J Yeh
language : en
Publisher: World Scientific
Release Date : 1995-12-08
Martingales And Stochastic Analysis written by James J Yeh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-08 with Mathematics categories.
This book is a thorough and self-contained treatise of martingales as a tool in stochastic analysis, stochastic integrals and stochastic differential equations. The book is clearly written and details of proofs are worked out.
Stochastic Integration And Differential Equations
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Author : Philip Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Stochastic Integration And Differential Equations written by Philip Protter 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 2013-04-17 with Mathematics categories.
The idea of this book began with an invitation to give a course at the Third Chilean Winter School in Probability and Statistics, at Santiago de Chile, in July, 1984. Faced with the problem of teaching stochastic integration in only a few weeks, I realized that the work of C. Dellacherie [2] provided an outline for just such a pedagogic approach. I developed this into aseries of lectures (Protter [6]), using the work of K. Bichteler [2], E. Lenglart [3] and P. Protter [7], as well as that of Dellacherie. I then taught from these lecture notes, expanding and improving them, in courses at Purdue University, the University of Wisconsin at Madison, and the University of Rouen in France. I take this opportunity to thank these institut ions and Professor Rolando Rebolledo for my initial invitation to Chile. This book assumes the reader has some knowledge of the theory of stochastic processes, including elementary martingale theory. While we have recalled the few necessary martingale theorems in Chap. I, we have not provided proofs, as there are already many excellent treatments of martingale theory readily available (e. g. , Breiman [1], Dellacherie-Meyer [1,2], or Ethier Kurtz [1]). There are several other texts on stochastic integration, all of which adopt to some extent the usual approach and thus require the general theory. The books of Elliott [1], Kopp [1], Metivier [1], Rogers-Williams [1] and to a much lesser extent Letta [1] are examples.
Introduction To Stochastic Integration
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Author : K.L. Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Introduction To Stochastic Integration written by K.L. Chung 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 2013-11-09 with Mathematics categories.
A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association An attractive text...written in [a] lean and precise style...eminently readable. Especially pleasant are the care and attention devoted to details... A very fine book. —Mathematical Reviews
Nonlinear Filtering And Smoothing
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Author : Venkatarama Krishnan
language : en
Publisher: Courier Corporation
Release Date : 2013-10-17
Nonlinear Filtering And Smoothing written by Venkatarama Krishnan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-17 with Science categories.
Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value. After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping times. Considerations of white noise and white-noise integrals are followed by examinations of stochastic integrals and stochastic differential equations, as well as the associated Ito calculus and its extensions. After defining the Stratonovich integral, the text derives the correction terms needed for computational purposes to convert the Ito stochastic differential equation to the Stratonovich form. Additional chapters contain the derivation of the optimal nonlinear filtering representation, discuss how the Kalman filter stands as a special case of the general nonlinear filtering representation, apply the nonlinear filtering representations to a class of fault-detection problems, and discuss several optimal smoothing representations.