Limit Theorems for Stochastic Processes (Hardcover)

~ (Author), Albert Shiryaev (Author) "The "General Theory of Stochastic Processes", in spite of its name, encompasses the rather restrictive subject of stochastic processes indexed by R+..." (more)
Key Phrases: strict stopping time, majoration condition, finite variation over finite intervals, Girsanov's Theorem, Progressive Conditional Continuous, Hence Theorem (more...)

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Product Description

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 integrals, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten.

Product Details

• Hardcover: 661 pages
• Publisher: Springer; 2nd edition (December 16, 2002)
• Language: English
• ISBN-10: 3540439323
• ISBN-13: 978-3540439325
• Product Dimensions: 9.4 x 6.1 x 1.6 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #854,313 in Books (See Bestsellers in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

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

By	Hossain Pezeshki - See all my reviews (REAL NAME)

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.