The Resource An Introduction to Infinite-Dimensional Analysis, by Giuseppe Da Prato, (electronic resource)

An Introduction to Infinite-Dimensional Analysis, by Giuseppe Da Prato, (electronic resource)

Label
An Introduction to Infinite-Dimensional Analysis
Title
An Introduction to Infinite-Dimensional Analysis
Statement of responsibility
by Giuseppe Da Prato
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
http://library.link/vocab/creatorName
Da Prato, Giuseppe
Dewey number
530.8
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
i7RLJEJv14g
Language note
English
LC call number
QA319-329.9
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Functional analysis
  • Distribution (Probability theory
  • Differential equations, partial
  • Functional Analysis
  • Probability Theory and Stochastic Processes
  • Partial Differential Equations
Label
An Introduction to Infinite-Dimensional Analysis, by Giuseppe Da Prato, (electronic resource)
Instantiates
Publication
Note
Introduction
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (215 p.)
Form of item
online
Isbn
9783540290216
Media category
computer
Media type code
  • c
Other control number
10.1007/3-540-29021-4
Specific material designation
remote
System control number
  • (CKB)1000000000282719
  • (EBL)3062622
  • (SSID)ssj0000318479
  • (PQKBManifestationID)11212538
  • (PQKBTitleCode)TC0000318479
  • (PQKBWorkID)10310817
  • (PQKB)11002005
  • (DE-He213)978-3-540-29021-6
  • (MiAaPQ)EBC3062622
  • (EXLCZ)991000000000282719
Label
An Introduction to Infinite-Dimensional Analysis, by Giuseppe Da Prato, (electronic resource)
Publication
Note
Introduction
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (215 p.)
Form of item
online
Isbn
9783540290216
Media category
computer
Media type code
  • c
Other control number
10.1007/3-540-29021-4
Specific material designation
remote
System control number
  • (CKB)1000000000282719
  • (EBL)3062622
  • (SSID)ssj0000318479
  • (PQKBManifestationID)11212538
  • (PQKBTitleCode)TC0000318479
  • (PQKBWorkID)10310817
  • (PQKB)11002005
  • (DE-He213)978-3-540-29021-6
  • (MiAaPQ)EBC3062622
  • (EXLCZ)991000000000282719

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