An Introduction to Infinite-Dimensional Analysis (Universitext) - Tapa blanda

From the reviews:

"This is an extended version of the author’s ‘An introduction to infinite-dimensional analysis’ published by Scuola Normale Superiore, Pisa ... . A well written textbook (even an introductory research monograph), suitable for teaching a graduate course." (Neils Jacob, Zentralblatt MATH, Vol. 1109 (11), 2007)

"The present volume collects together ... the notes of the course on infinite-dimensional analysis held by the author at the Scuola Normale Superiore of Pisa in recent years. The book is intended for people who have some knowledge of functional analysis ... . It provides an extremely useful tool for those scholars who are interested in learning some basics about Gaussian measures in Hilbert spaces, Brownian motion, Markov transition semigroups ... . The book is well written and all arguments are clearly and rigorously presented." (Sandra Cerrai, Mathematical Reviews, Issue 2009 a)

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.