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

  • Authors
  • Nikolai A. Krylov
  • Jerzy Zabczyk
  • Michael Röckner
  • Editors
  • Giueppe Da Prato

Part of the Lecture Notes in Mathematics book series (LNM, volume 1715)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. J. Zabczyk
    Pages 117-239
  3. Back Matter
    Pages 242-242

About this book

Introduction

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.

Keywords

Dirichlet form Dirichlet forms Gaussian measure Kolmogorov equations Markov property Martingale Ornstein-Uhlenbeck process Stochastic calculus

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092416
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66545-8
  • Online ISBN 978-3-540-48161-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book