Second Order PDE's in Finite and Infinite Dimension A Probabilistic Approach /

• Main Author: Cerrai, Sandra (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1762
• Subjects: Partial differential equations.; Probabilities.; Partial Differential Equations.; Probability Theory and Stochastic Processes.

The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transit...

Table of Contents:

• Kolmogorov equations in Rd with unbounded coefficients
• Asymptotic behaviour of solutions
• Analyticity of the semigroup in a degenerate case
• Smooth dependence on data for the SPDE: the Lipschitz case
• Kolmogorov equations in Hilbert spaces
• Smooth dependence on data for the SPDE: the non-Lipschitz case (I)
• Smooth dependence on data for the SPDE: the non-Lipschitz case (II)
• Ergodicity
• Hamilton- Jacobi-Bellman equations in Hilbert spaces
• Application to stochastic optimal control problems.