Second Order PDE's in Finite and Infinite Dimension - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Second Order PDE's in Finite and Infinite Dimension write by Sandra Cerrai. This book was released on 2003-07-01. Second Order PDE's in Finite and Infinite Dimension available in PDF, EPUB and Kindle. 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.
Second Order Pde's in Finite and Infinite Dimension
Second Order Pde's in Finite and Infinite Dimension - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Second Order Pde's in Finite and Infinite Dimension write by Sandra Cerrai. This book was released on 2014-09-01. Second Order Pde's in Finite and Infinite Dimension available in PDF, EPUB and Kindle.
Stochastic Optimal Control in Infinite Dimension
Stochastic Optimal Control in Infinite Dimension - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Optimal Control in Infinite Dimension write by Giorgio Fabbri. This book was released on 2017-06-22. Stochastic Optimal Control in Infinite Dimension available in PDF, EPUB and Kindle. Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Second Order Partial Differential Equations in Hilbert Spaces
Second Order Partial Differential Equations in Hilbert Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Second Order Partial Differential Equations in Hilbert Spaces write by Giuseppe Da Prato. This book was released on 2002-07-25. Second Order Partial Differential Equations in Hilbert Spaces available in PDF, EPUB and Kindle. State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.
Stochastic Equations in Infinite Dimensions
Stochastic Equations in Infinite Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Equations in Infinite Dimensions write by Giuseppe Da Prato. This book was released on 2014-04-17. Stochastic Equations in Infinite Dimensions available in PDF, EPUB and Kindle. Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
