Lecture Notes of the Unione Matematica Italiana

Hyperfinite Dirichlet Forms and Stochastic Processes

Authors: Albeverio, Sergio, Fan, Ruzong, Herzberg, Frederik S.

  • Includes historical notes and comprehensive bibliography
  • An appendix on nonstandard analysis makes the book self-contained
  • A special chapter on Lévy processes increases the scope of applications
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About this book

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.


Reviews

From the reviews:

“This book deals with the relationship between Dirichlet forms and stochastic processes from the perspective of nonstandard analysis. … The book has a very extensive bibliography and gives an interesting and valuable survey of the development and the applications of the theory of Dirichlet forms. … the book will serve as a starting point for new explorations.” (Tom L. Lindström, Mathematical Reviews, Issue 2012 k)


Table of contents (6 chapters)

  • Hyperfinite Dirichlet Forms

    Albeverio, Sergio (et al.)

    Pages 1-63

  • Potential Theory of Hyperfinite Dirichlet Forms

    Albeverio, Sergio (et al.)

    Pages 65-128

  • Standard Representation Theory

    Albeverio, Sergio (et al.)

    Pages 129-163

  • Construction of Markov Processes Associated With Quasi-Regular Dirichlet Forms

    Albeverio, Sergio (et al.)

    Pages 165-198

  • Hyperfinite Lévy Processes

    Albeverio, Sergio (et al.)

    Pages 199-241

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-19659-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-19658-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Hyperfinite Dirichlet Forms and Stochastic Processes
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
10
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-19659-1
DOI
10.1007/978-3-642-19659-1
Softcover ISBN
978-3-642-19658-4
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XIV, 284
Number of Illustrations and Tables
1 illustrations in colour
Topics