Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorKrylov, Nikolai A. author
TitleStochastic PDE's and Kolmogorov Equations in Infinite Dimensions [electronic resource] : 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 / by Nikolai A. Krylov, Jerzy Zabczyk, Michael Rรถckner ; edited by Giueppe Da Prato
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1999
Connect tohttp://dx.doi.org/10.1007/BFb0092416
Descript XII, 244 p. online resource

SUMMARY

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. Rรถckner 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


CONTENT

N.V. Krylov: On Kolmogorov's equations for finite dimensional diffusions: Solvability of Ito's stochastic equations; Markov property of solution; Conditional version of Kolmogorov's equation; Differentiability of solutions of stochastic equations with respect to initial data; Kolmogorov's equations in the whole space; Some Integral approximations of differential operators; Kolmogorov's equations in domains -- M. Roeckner: LP-analysis of finite and infinite dimensional diffusion operators: Solution of Kolmogorov equations via sectorial forms; Symmetrizing measures; Non-sectorial cases: perturbations by divergence free vector fields; Invariant measures: regularity, existence and uniqueness; Corresponding diffusions and relation to Martingale problems -- J. Zabczyk: Parabolic equations on Hilbert spaces: Heat equation; Transition semigroups; Heat equation with a first order term; General parabolic equations; Regularity and Quiqueness; Parabolic equations in open sets; Applications


Mathematics Partial differential equations Probabilities Mathematics Probability Theory and Stochastic Processes Partial Differential Equations



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram