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Introduction to the Theory of (Non-Symmetric) Dirichlet Forms

The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and the probabilistic part of the theory up to and including the construction of an associated Markov process. It is base...

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Bibliographic Details
Main Authors: Ma, Zhi-Ming, Röckner, Michael (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1992, 1992
Edition:1st ed. 1992
Series:Universitext
Subjects:
Potential Theory (mathematics)
Potential Theory
Probability Theory And Stochastic Processes
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 0 Introduction
  • I Functional Analytic Background
  • 1 Resolvents, semigroups, generators
  • 2 Coercive bilinear forms
  • 3 Closability
  • 4 Contraction properties
  • 5 Notes/References
  • II Examples
  • 1 Starting point: operator
  • 2 Starting point: bilinear form — finite dimensional case
  • 3 Starting point: bilinear form — infinite dimensional case
  • 4 Starting point: semigroup of kernels
  • 5 Starting point: resolvent of kernels
  • 6 Notes/References
  • III Analytic Potential Theory of Dirichlet Forms
  • 1 Excessive functions and balayage
  • 2 ?-exceptional sets and capacities
  • 3 Quasi-continuity
  • 4 Notes/References
  • IV Markov Processes and Dirichlet Forms
  • 1 Basics on Markov processes
  • 2 Association of right processes and Dirichlet forms
  • 3 Quasi-regularity and the construction of the process
  • 4 Examples of quasi-regular Dirichlet forms
  • 5 Necessity of quasi-regularity and some probabilistic potential theory
  • 6 One-to-one correspondences
  • 7 Notes/References
  • V Characterization of Particular Processes
  • 1 Local property and diffusions
  • 2 A new capacity and Hunt processes
  • 3 Notes/References
  • VI Regularization
  • 1 Local compactification
  • 2 Consequences — the transfer method
  • 3 Notes/References
  • A Some Complements
  • 1 Adjoint operators
  • 2 The Banach/Alaoglu and Banach/Saks theorems
  • 3 Supplement on Ray resolvents and right processes

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