Gaussian Measures (Mathematical Surveys and Monographs)
| Author | : | |
| Rating | : | 4.59 (796 Votes) |
| Asin | : | 0821810545 |
| Format Type | : | paperback |
| Number of Pages | : | 433 Pages |
| Publish Date | : | 2016-11-11 |
| Language | : | English |
DESCRIPTION:
Bogachev , Moscow State University, Russia. . Vladimir I
"This will be a classic work on measure theory" according to Terence Mills. The author is a mathematician from Moscow who specialises in measure theory. It is a book on advanced mathematics - you can read the inside of it. Anyway, the book has been well written, with lots of exercises and copious historical notes. I can also recommend his two-volume treatise "Measure Theory". If your library has Halmos' classic work then you might consider adding these works by Bogachev as well. They will be classics.. First chapter on d-dimensional Gaussian measures worth reading by itself Jordan Bell Most of the book is on Gaussian measures generally on locally convex spaces. From the scattered reading I've done, that there are few expositions on this. Although Bogachev is writing about machinery with many moving parts, he writes in a nice pedestrian way, and rather than asserting things to be trivial that are messy to write out he either gets his hands dirty or cites a proof, which at least lets the reader know that the result is not meant to be obvious. In the second chapter Bogachev talks about the Cameron-Martin space. However, because locally convex spaces are not as securely in the arsenal of analysts as they ought to be, I
It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. This book gives a systematic exposition of the modern theory of Gaussian measures. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.
A deep and detailed treatment of an important subject. --American Mathematical Monthly