{"product_id":"an-introduction-to-infinite-dimensional-analysis-9783642421686","title":"An Introduction to Infinite-Dimensional Analysis","description":"\u003cp\u003e • Author(s): Giuseppe Da Prato\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Probability \u0026amp; Statistics - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eIn 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. \u003c\/p\u003e \u003cp\u003eStarting 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45274609516695,"sku":"9783642421686","price":3639.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783642421686.webp?v=1769280433","url":"https:\/\/atlanticbooks.com\/products\/an-introduction-to-infinite-dimensional-analysis-9783642421686","provider":"Atlantic Books","version":"1.0","type":"link"}