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Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetraro, Italy, August 24 - September 1, 1998

  • Book
  • © 1999

Overview

Authors:
  1. Nikolai A. Krylov
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  2. Jerzy Zabczyk
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  3. Michael Röckner
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Editors:
  1. Giueppe Prato
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1715)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-VIII
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  2. On Kolmogorov’s equations for finite dimensional diffusions

    • N. V. Krylov
    Pages 1-63

  3. Lp-analysis of finite and infinite dimensional diffusion operators

    • Michael Röckner
    Pages 65-116

  4. Parabolic equations on Hilbert spaces

    • J. Zabczyk
    Pages 117-239

  5. Back Matter

    Pages 242-242
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Keywords

About this book

Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.

Bibliographic Information

  • Book Title: Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

  • Book Subtitle: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetraro, Italy, August 24 - September 1, 1998

  • Authors: Nikolai A. Krylov, Jerzy Zabczyk, Michael Röckner

  • Editors: Giueppe Prato

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0092416

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-66545-8Published: 19 October 1999

  • eBook ISBN: 978-3-540-48161-4Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 244

  • Topics: Probability Theory and Stochastic Processes, Partial Differential Equations

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