Mathematical Surveys and Monographs 1998; 433 pp; hardcover Volume: 62 ISBN10: 0821810545 ISBN13: 9780821810545 List Price: US$116 Member Price: US$92.80 Order Code: SURV/62
 This book gives a systematic exposition of the modern theory of Gaussian measures. 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. 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. Readership Graduate students, research mathematicians, and mathematical physicists working in probability, statistics, and analysis. Reviews "A deep and detailed treatment of an important subject."  American Mathematical Monthly "The scope of topics related to Gaussian processes and measures is huge. Complemented by a list of problems in each chapter, a collection of over 800 references and a detailed section of bibliographical comments, Bogachev's book covers, in varying degrees of detail, an impressive portion of the theoretical part of this scope. It does so in a clear and precise mathematical style."  Mathematical Reviews Table of Contents  Finite dimensional Gaussian distributions
 Infinite dimensional Gaussian distributions
 Radon Gaussian measures
 Convexity of Gaussian measures
 Sobolev classes over Gaussian measures
 Nonlinear transformations of Gaussian measures
 Applications
 Locally convex spaces, operators, and measures
 Bibliographical comments
 References
 Index
