Lecture Notes in Mathematics

Second Order PDE's in Finite and Infinite Dimension

A Probabilistic Approach

Authors: Cerrai, Sandra

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About this book

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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-540-45147-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-3-540-42136-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Second Order PDE's in Finite and Infinite Dimension
Book Subtitle
A Probabilistic Approach
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1762
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45147-1
DOI
10.1007/b80743
Softcover ISBN
978-3-540-42136-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 332
Topics