Multidimensional Diffusion Processes (Graduate Texts in Mathematics) - Hardcover

Daniel W. Stroock

Hardcover

ISBN 10: 0387903534 ISBN 13: 9780387903538

Publisher: Springer-Verlag Telos, 1979

Synopsis

The series "Grundlehren der mathematischen Wissenschaften" (subtitled Comprehensive Studies in Mathematics), Springer's first series in higher mathematics, was founded by Richard Courant in 1920. The Grundlehren were conceived as a series of modern textbooks. This character is obvious in the first 60-70 volumes, but the series underwent a number of significant changes after World War II. Outwardly, the change was in language. Whereas the overwhelming majority of the first 100 volumes were published in German, the following volumes are nearly all in English. A more important change concerns the contents of the books. The original objective of the Grundlehren had been to lead students to the principal results and to recent research questions in a single relatively elementary and easily readable book.

About this title

From the Back Cover:

From the reviews:

"... Both the Markov-process approach and the Itô approach ... have been immensely successful in diffusion theory. The Stroock-Varadhan book, developed from the historic 1969 papers by its authors, presents the martingale-problem approach as a more powerful - and, in certain regards, more intrinsic-means of studying the foundations of the subject. [...] ... the authors make the uncompromising decision not "to proselytise by intimidating the reader with myriad examples demonstrating the full scope of the techniques", but rather to persuade the reader "with a careful treatment of just one problem to which they apply". [...] Most of the main tools of stochastic-processes theory are used, ..but it is the formidable combination of probability theory with analysis ... which is the core of the work. [...] I have emphasized the great importance of the Stroock-Varadhan book. It contains a lot more than I have indicated; in particular, its many exercises conain much interesting material.
For immediate confirmation of the subject’s sparkle, virtuosity, and depth, see ... McKean (‘s 1969 book). The Stroock-Varadhan book proceeds on its inexorable way like a massive Bach fugue. ... But old J.S. can e something of knockout if his themes get hold of you. And his influence on what followed was 8you may say) substantial."
David Williams in the Bulletin of the American Mathematical Society

About this edition

• Publisher: Springer-Verlag Telos
• Publication date: 1979
• ISBN 10: 0387903534
• ISBN 13: 9780387903538
• Binding: Hardcover
• Number of pages: 338