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978-3-540-29021-6
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100301s2006 gw | s |||| 0|eng d
9783540290216
978-3-540-29021-6
10.1007/3-540-29021-4
doi
ISI Library, Kolkata
QA319-329.9
PBKF
bicssc
MAT037000
bisacsh
PBKF
thema
515.7
23
Prato, Giuseppe Da.
author.
aut
http://id.loc.gov/vocabulary/relators/aut
An Introduction to Infinite-Dimensional Analysis
[electronic resource] /
by Giuseppe Da Prato.
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2006.
X, 208 p.
online resource.
text
txt
rdacontent
computer
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rdamedia
online resource
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text file
PDF
rda
Universitext,
0172-5939
Gaussian measures in Hilbert spaces -- The Cameron–Martin formula -- Brownian motion -- Stochastic perturbations of a dynamical system -- Invariant measures for Markov semigroups -- Weak convergence of measures -- Existence and uniqueness of invariant measures -- Examples of Markov semigroups -- L2 spaces with respect to a Gaussian measure -- Sobolev spaces for a Gaussian measure -- Gradient systems.
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.
Functional analysis.
Distribution (Probability theory.
Differential equations, partial.
Functional Analysis.
http://scigraph.springernature.com/things/product-market-codes/M12066
Probability Theory and Stochastic Processes.
http://scigraph.springernature.com/things/product-market-codes/M27004
Partial Differential Equations.
http://scigraph.springernature.com/things/product-market-codes/M12155
SpringerLink (Online service)
Springer eBooks
Printed edition:
9783540815907
Printed edition:
9783540290209
Printed edition:
9783642421686
Universitext,
0172-5939
https://doi.org/10.1007/3-540-29021-4
ZDB-2-SMA
EB
Mathematics and Statistics (Springer-11649)
425240
425240