| Analytical Methods for Markov Semigroups Contributor(s): Lorenzi, Luca (Author), Bertoldi, Marcello (Author) |
|
 |
ISBN: 1584886595 ISBN-13: 9781584886594 Publisher: CRC Press OUR PRICE: $156.75 Product Type: Hardcover - Other Formats Published: August 2006 Annotation: Analytical Methods for Markov Semigroups provides a comprehensive analysis on Markov semigroups both in spaces of bounded and continuous functions as well as in Lp spaces relevant to the invariant measure of the semigroup. The book covers Schauder's estimates for nonhomogeneous elliptic and parabolic problems and for degenerate elliptic operators modeled on the Ornstein-Uhlenbeck operator, and includes in-depth analysis of Markov semigroups associated with elliptic operators that have unbounded coefficients in unbounded domains. It also features nondegenerate and degenerate Ornstein-Uhlenbeck operators, as well as contains classical results of functional analysis and classical theory of partial differential equations. |
| Additional Information |
| BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Differential Equations - General - Mathematics | Probability & Statistics - Bayesian Analysis |
| Dewey: 512.27 |
| LCCN: 2006045837 |
| Series: Pure and Applied Mathematics |
| Physical Information: 1.36" H x 6.3" W x 9.08" (1.92 lbs) 526 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: For the first time in book form, Analytical Methods for Markov Semigroups provides a comprehensive analysis on Markov semigroups both in spaces of bounded and continuous functions as well as in Lp spaces relevant to the invariant measure of the semigroup. Exploring specific techniques and results, the book collects and updates the literature associated with Markov semigroups. Divided into four parts, the book begins with the general properties of the semigroup in spaces of continuous functions: the existence of solutions to the elliptic and to the parabolic equation, uniqueness properties and counterexamples to uniqueness, and the definition and properties of the weak generator. It also examines properties of the Markov process and the connection with the uniqueness of the solutions. In the second part, the authors consider the replacement of RN with an open and unbounded domain of RN. They also discuss homogeneous Dirichlet and Neumann boundary conditions associated with the operator A. The final chapters analyze degenerate elliptic operators A and offer solutions to the problem. Using analytical methods, this book presents past and present results of Markov semigroups, making it suitable for applications in science, engineering, and economics. |