Limit Theorems for Stochastic Processes

• 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.

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 Lepingle, 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)