Springer The Generic Chaining: Upper and Lower Bounds of Stochastic Processes (Springer Monographs in Mathematics)

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain. Review From the reviews: "This textbook gives a systematic approach to the problem of deriving good bounds for stochastic processes using the ‘generic chaining’ method … . The presentation in this book … takes the reader from a simple and intuitive explanation of the basic idea underlying the chaining technique to the edge of today’s knowledge. … The entertaining and sometimes humorous style makes this book a pleasure to read." (Dierk Peithmann, Zentralblatt MATH, Vol. 1075, 2006) "The results discussed in the book involve a tremendous amount of creativity … . I believe that the monograph is of interest to anyone who works even remotely with indexed families of maps… . is of interest to almost everyone who works in probability, analysis, or ergodic theory even if she/he has not done any research involving the topics covered by the volume under review. … I want to emphasize the fact that the book is of interest to a larger audience … ." (Radu Zaharopol, SIAM Review, Vol. 49 (2), 2007)