Limit Theorems for Stochastic Processes (Grundlehren Der Mathematischen Wissenschaften) [Hardcover]

Jean Jacod (Author), Albert Nikolaevich Shiriaev (Author)

Book Description

ISBN-10: 0387178821 | ISBN-13: 978-0387178820 | Publication Date: November 1987

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.

Editorial Reviews

Review

From the reviews of the second edition:

"This is the second edition of a well-known book. Fifteen years ago, the first edition … proved essential for all people interested in functional convergence of stochastic processes. … Some new materials have been included in the present edition. … There is also an up-to-date account on predictable uniform tightness because there has been significant progress in this field since the first edition. No doubt that this book will continue being a necessary companion for stochasticians." (Dominique Lépingle, Mathematical Reviews, 2003 j)

"This is the second edition of the fundamental monograph … . This new edition has grown by about 50 pages … . These extensions make the book even more valuable and comprehensive for people working in mathematical finance, numerics of stochastic processes and, of course, statistics of stochastic processes." (Markus Reiß, Zentralblatt MATH, Vol. 1018, 2003)

"The 1987 version of the book was a landmark in probability theory. The same can be said about the second edition. I can recommend this book to every reader who is sufficiently experienced and willing to spend some effort … . Also, I think the book is very useful as a reference. … To conclude, this book is still the reference in this domain and as such I can definitely recommend it to both pure and applied probabilists who are interested in this topic." (A.P. Zwart, Nieuw Archief voor Wiskunde, Vol. 7 (2), 2006)

--This text refers to an alternate Hardcover edition.

From the Back Cover

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students. --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 600 pages
• Publisher: Springer-Verlag (November 1987)
• Language: English
• ISBN-10: 0387178821
• ISBN-13: 978-0387178820
• Product Dimensions: 9.8 x 6.8 x 1.2 inches
• Shipping Weight: 2.3 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #5,322,905 in Books (See Top 100 in Books)

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4 of 4 people found the following review helpful:

4.0 out of 5 stars A superb harmony, February 22, 2007

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Hossain Pezeshki "Dr. Hossain Pezeshk-Esfahani" - See all my reviews
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This review is from: Limit Theorems for Stochastic Processes (Hardcover)

Just about every time I open this book I either find the elucidation of a concept which either I have always wanted to learn; or see the connection between ideas which I have known for some time.
This valuable work unifies a number of topics which are of great importance to the mathematical practitioner. Each of these is treated not merely as noetic nicety but as tool for applying the theory.
The thorough and extensive treatment of continguity theory for point processes and convergence of stochastic integrals are especially well done and satisfying.
Although even a two semester course does not suffice to cover the entire book I nevertheless feel that the dedicated educator should be able to delineate a number of threads for two one-semeter graduate courses.