Stochastic Integration and Differential Equations: A New Approach (Stochastic Modelling and Applied Probability, 21)

Protter, Philip:

ISBN 10: 3540509968 / ISBN 13: 9783540509967

Published by Springer, 1990

About this Item

312 Seiten; 9783540509967.4 Gewicht in Gramm: 1.

Seller Inventory # 883172

Bibliographic Details

• Title: Stochastic Integration and Differential Equations: A New Approach (Stochastic Modelling and Applied Probability, 21)
• Publisher: Springer
• Publication Date: 1990
• Language: English
• ISBN 10: 3540509968
• ISBN 13: 9783540509967
• Binding: paperback
• Condition: Befriedigend
• Seller catalogs:
  • Varia

About this title

Synopsis

This book is quite different from others on the subject in that it presents a rapid introduction to the modern semimartingale theory of stochastic integration and differential equations, without first having to treat the beautiful but highly technical "general theory of processes". The author's new approach (based on the theorem of Bitcheler-Dellacherie) also give a more intuitive understanding of the subject, and permits proofs to be much less technical. All of the major theorems of stochastic integration are given, including a comprehensive treatment (first time in English) of local times. A theory of stochastic differential equations driven by semimartingales is developed, including Fisk-Stratonovich equations, Markov properties, stability, and an introduction to the theory of flows. Further topics presented for the 1st time in book form include an elementary presentation of Azema's martingale. This book will quickly become a standard reference on the subject, to be used by specialists and non-specialists alike, both for the sake of the theory and for its application.

Review

From the reviews of the second edition:

"A fast and nice introduction to semimartingales and stochastic integration ... . The second edition of the book has a number of changes and new topics ... . The book is highly recommendable for graduate students and experts alike. It is a pleasure to read, with many examples, and all arguments are presented clearly and with care. This book can equally well serve as a course on stochastic calculus as well as an excellent reference material." (Prof. Dr. M. Vanmaele, KWANT METHODEN, 2004)

"It has been well over a decade ... . the second edition, particularly since the book itself has by now become a well-known and often-used classic. ... While the second edition follows the outline and content of the first edition quite closely ... . The book is carefully written and well presented and covers the topics of stochastic integration ... . The changes and additions have served to make this now classic "new approach" only a more attractive and comprehensive entry point ... ." (Anja Sturm, SIAM Review Vol. 47(1), 2005)

"As anyone who has taught or attended a course on Stochastic calculus knows, one of the most difficult aspect of the theme is absence of exercises in the books on the topic. The second edition of this book comes to the rescue. Each chapter has exercises which should help instructors and students alike. ... This book would serve as a good text for a course on stochastic calculus. At the same time, it is also a good reference book." (Rajeeva L. Karandikar, Sankhya: The Indian Journal of Statistics, Vol. 66 (1), 2004)

"In this new edition several changes have been made; most of them are inclusions of results obtained since the appearance of the first edition ... . addition is exercises, to be found at the end of each chapter. Altogether I agree with the previous reviewer ... the book provides an excellent basis for lecturing or self teaching." (Evelyn Buckwar, Mathematical Reviews, Issue 2005 k)