Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

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. L^p-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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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.

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

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