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

Cerrai, Sandra

ISBN 10: 354042136X / ISBN 13: 9783540421368

Published by Springer 2001-06, 2001

About this Item

Seller Inventory # 6666-IUK-9783540421368

Bibliographic Details

• Title: Second Order PDE's in Finite and Infinite Dimension : A Probabilistic Approach
• Publisher: Springer 2001-06
• Publication Date: 2001
• Language: English
• ISBN 10: 354042136X
• ISBN 13: 9783540421368
• Binding: PF
• Condition: New

About this title

Synopsis

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 transition semigroups in the space of bounded and uniformly continuous functions. As an application of these results, we study the associated Kolmogorov equations, the large-time behaviour of the solutions and some stochastic optimal control problems together with the corresponding Hamilton- Jacobi-Bellman equations. In the literature there exists a large number of works (mostly in finite dimen­ sion) dealing with these arguments in the case of bounded Lipschitz-continuous coefficients and some of them concern the case of coefficients having linear growth. Few papers concern the case of non-Lipschitz coefficients, but they are mainly re­ lated to the study of the existence and the uniqueness of solutions for the stochastic system. Actually, the study of any further properties of those systems, such as their regularizing properties or their ergodicity, seems not to be developed widely enough. With these notes we try to cover this gap.