Limit Theorems for Stochastic Processes / Edition 2

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This volume by two international leaders in the field proposes a systematic exposition of convergence in law for shastic 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 shastic processes, such as martingale problems and absolute continuity or contiguity results.

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Editorial Reviews

From the Publisher
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 shastic 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 shasticians." (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 shastic processes and, of course, statistics of shastic 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)

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Product Details

  • ISBN-13: 9783642078767
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/1/2010
  • Series: Grundlehren der mathematischen Wissenschaften Series, #288
  • Edition description: Softcover reprint of hardcover 2nd ed. 2003
  • Edition number: 2
  • Pages: 664
  • Product dimensions: 1.38 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

I. The General Theory of Shastic Processes, Semimartingales and Shastic 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.

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