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.
"synopsis" may belong to another edition of this title.
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension.
Starting 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 some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
GIUSEPPE DA PRATO was born in La Spezia in 1936. Having graduated in Physics in 1960 from the University of Rome, he became full professor of Mathematics in 1968 and taught in Rome and in Trento. Since 1979 he has been Professor of Mathematical Analysis at the Scuola Normale Superiore di Pisa.
The scientific activity of Giuseppe Da Prato concerns infinite-dimensional analysis and partial differential stochastic equations (existence, uniqueness, invariant measures, ergodicity), with applications to optimal stochastic control.
Giuseppe Da Prato is the author of 5 other books, some co-authored with other international specialists, on control theory, stochastic differential equations and infinite dimensional Kolmogorov equations, and of more than 250 papers in international scientific journals.
"About this title" may belong to another edition of this title.
Shipping:
FREE
Within U.S.A.
Book Description Condition: New. Book is in NEW condition. Seller Inventory # 3540290206-2-1
Book Description Condition: New. New! This book is in the same immaculate condition as when it was published. Seller Inventory # 353-3540290206-new
Book Description Condition: Brand New. New. US edition. Expediting shipping for all USA and Europe orders excluding PO Box. Excellent Customer Service. Seller Inventory # ABEOCT23-189539
Book Description Condition: New. Brand New Original US Edition.We Ship to PO BOX Address also. EXPEDITED shipping option also available for faster delivery.This item may ship from the US or other locations in India depending on your location and availability. Seller Inventory # ABTR-216453
Book Description Condition: New. Brand New Original US Edition. Customer service! Satisfaction Guaranteed. This item may ship from the US or our Overseas warehouse depending on your location and stock availability. We Ship to PO BOX Location also. Seller Inventory # ABRR-216453
Book Description Soft Cover. Condition: new. Seller Inventory # 9783540290209
Book Description Condition: New. pp. 228. Seller Inventory # 26288064
Book Description Condition: New. Seller Inventory # ABLIING23Mar3113020164779
Book Description Condition: New. pp. 228 Illus. Seller Inventory # 7592607
Book Description Condition: New. PRINT ON DEMAND Book; New; Fast Shipping from the UK. No. book. Seller Inventory # ria9783540290209_lsuk