Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions
Subtitle: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held ... Mathematics / Fondazione C.I.M.E., Firenze)
Contributors: G. Da Prato (Editor)
Edition: 1 edition
Publisher: Springer
Published: December 15, 1999
Language: eng
Format: Paperback
Number of pages: 239
ISBN-13: 9783540665458
Subjects: Differential Equations; Probability & statistics; Science/Mathematics; Stochastic Processes; Time Series Analysis; Mathematics; Stochastic partial differential equations; Probability & Statistics - General; Dirichlet forms; Kolmogorov equations; Mathematics / Statistics; Mathematics-Differential Equations; Ornstein-Uhlenbeck process; Diffusion processes; Gaussian processes; Stochastic partial differentia
Description: 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.