Some random series of functions. 2nd ed. (English) Zbl 0571.60002

Kahane, Jean-Pierre

Cambridge Studies in Advanced Mathematics, 5. Cambridge etc.: Cambridge University Press. xiii, 305 p. £30.00; $ 47.50 (1985).

It is a great joy to see this book the first edition of which appeared in 1968, see Zbl 0192.53801, available again after being out of print for so many years. It has stimulated a great deal of work over the past fifteen years, both in Fourier series and in random processes and the task of distilling a second edition from the multitude of new results is far from easy. Most of the new material concerns random processes and the 5 new chapters cover Hausdorff measures and dimensions, random translates and coverings, boundedness and continuity of Gaussian processes, path properties of Brownian motion, and Hausdorff measures, level sets and occupation densities for fractional Brownian processes. There are also new sections in original chapters, but most of the original material remains. The second edition is about 50% larger than the first and is a very readable account of the interplay between classical real function theory and stochastic processes.

Reviewer: J. Cuzick

MSC:

60-02	Research exposition (monographs, survey articles) pertaining to probability theory
60G15	Gaussian processes
60J65	Brownian motion
60G17	Sample path properties

Keywords:

Fourier series; Hausdorff measures and dimensions; continuity of Gaussian processes; path properties; fractional Brownian processes

Citations:

Zbl 0192.53801