Limit Theorems for Stochastic Processes

Jean Jacod, Albert Shiryaev (Autoren)

Buch | Softcover

XX, 664 Seiten

2010 | 2. Softcover reprint of hardcover 2nd ed. 2003
Springer Berlin (Verlag)
978-3-642-07876-7 (ISBN)

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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 asa 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.

I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems and Changes of Measures.- IV. Hellinger Processes, Absolute Continuity and Singularity of Measures.- V. Contiguity, Entire Separation, Convergence in Variation.- VI. Skorokhod Topology and Convergence of Processes.- VII. Convergence of Processes with Independent Increments.- VIII. Convergence to a Process with Independent Increments.- IX. Convergence to a Semimartingale.- X. Limit Theorems, Density Processes and Contiguity.- Bibliographical Comments.- References.- Index of Symbols.- Index of Terminology.- Index of Topics.- Index of Conditions for Limit Theorems.

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)

Erscheint lt. Verlag	18.12.2010
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Zusatzinfo	XX, 664 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1020 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	absolute continuity • central limit theorem • contiguity • convergence of processes • diffusion process • Martingale • random measure • semimartingale • semimartingales • Statistics • stochastic integrals • Stochastic process • Stochastic Processes
ISBN-10	3-642-07876-1 / 3642078761
ISBN-13	978-3-642-07876-7 / 9783642078767
Zustand	Neuware