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Analytical methods for Markov semigroups 1st Edition by Luca Lorenzi, Marcello Bertoldi ISBN 1584886595 9781584886594

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Analytical methods for Markov semigroups 1st Edition Luca Lorenzi Digital Instant Download

Author(s): Luca Lorenzi, Marcello Bertoldi
ISBN(s): 9781584886594, 1584886595
Edition: 1
File Details: PDF, 2.53 MB
Year: 2007
Language: english
SKU: EB-1008404 Category: Tags: ,

Analytical methods for Markov semigroups 1st Edition by Luca Lorenzi, Marcello Bertoldi – Ebook PDF Instant Download/Delivery: 1584886595, 9781584886594
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Product details:

ISBN 10: 1584886595 
ISBN 13: 9781584886594
Author: Luca Lorenzi, Marcello Bertoldi

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.

Analytical methods for Markov semigroups 1st Table of contents:

Part I: Markov Semigroups in ℝⁿ

  1. Introduction

  2. The Elliptic Equation and the Cauchy Problem in Cᵦ(ℝⁿ): The Uniformly Elliptic Case

  3. One‑Dimensional Theory

  4. Uniqueness Results, Conservation of Probability and Maximum Principles

  5. Properties of T(t) in Spaces of Continuous Functions

  6. Uniform Estimates for the Derivatives of T(t)f

  7. Pointwise Estimates for the Derivatives of T(t)f

  8. Invariant Measures µ and the Semigroup in Lᵖ(ℝⁿ, µ)

  9. The Ornstein–Uhlenbeck Operator

  10. A Class of Nonanalytic Markov Semigroups in Cᵦ(ℝⁿ) and Lᵖ(ℝⁿ, µ)

Part II: Markov Semigroups in Unbounded Open Sets

  1. The Cauchy–Dirichlet Problem

  2. The Cauchy–Neumann Problem: The Convex Case

  3. The Cauchy–Neumann Problem: The Nonconvex Case

Part III: Degenerate-Elliptic-Operator Semigroups in ℝⁿ

  1. The Cauchy Problem in Cᵦ(ℝⁿ)

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Tags: Luca Lorenzi, Marcello Bertoldi, Analytical methods, Markov semigroups