Stochastic Integration and Differential Equations

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)

• I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic Differential Equations.- VI Expansion of Filtrations.- References.