Hyperfinite Dirichlet Forms and Stochastic Processes

  • Sergio Albeverio
  • Ruzong Fan
  • Frederik Herzberg

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 10)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sergio Albeverio, Ruzong Fan, Frederik Herzberg
    Pages 1-63
  3. Sergio Albeverio, Ruzong Fan, Frederik Herzberg
    Pages 65-128
  4. Sergio Albeverio, Ruzong Fan, Frederik Herzberg
    Pages 129-163
  5. Sergio Albeverio, Ruzong Fan, Frederik Herzberg
    Pages 165-198
  6. Sergio Albeverio, Ruzong Fan, Frederik Herzberg
    Pages 199-241
  7. Sergio Albeverio, Ruzong Fan, Frederik Herzberg
    Pages 243-248
  8. Back Matter
    Pages 249-285

About this book

Introduction

This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces.
 
The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.


Keywords

03H05; 60J45 Dirichlet form Markov processes non-standard analysis

Authors and affiliations

  • Sergio Albeverio
    • 1
  • Ruzong Fan
    • 2
  • Frederik Herzberg
    • 3
  1. 1.Institute of Applied MathematicsUniversity of BonnBonnGermany
  2. 2.Department of StatisticsTexas A&M UniversityCollege StationUSA
  3. 3.Institute of Mathematical EconomicsBielefeld UniversityBielefeldGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-19659-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-19658-4
  • Online ISBN 978-3-642-19659-1
  • Series Print ISSN 1862-9113
  • About this book