Limit Theorems for Stochastic Processes 2nd Edition by Jean Jacod (PDF)

Description

This volume by two international leaders in the field proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. It emphasizes results that are useful for mathematical theory and mathematical statistics. Coverage develops in detail useful parts of the general theory of stochastic processes, such as martingale problems and absolute continuity or contiguity results.

User’s Reviews

Editorial Reviews: Review as 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) 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

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