Author | Krylov, Nikolai A. author |
---|---|
Title | Stochastic 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 |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1999 |
Connect to | http://dx.doi.org/10.1007/BFb0092416 |
Descript | XII, 244 p. online resource |
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