Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 10)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Hyperfinite Dirichlet Forms and Stochastic Processes
Authors: Sergio Albeverio, Ruzong Fan, Frederik Herzberg
Series Title: Lecture Notes of the Unione Matematica Italiana
DOI: https://doi.org/10.1007/978-3-642-19659-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Softcover ISBN: 978-3-642-19658-4Published: 29 May 2011
eBook ISBN: 978-3-642-19659-1Published: 27 May 2011
Series ISSN: 1862-9113
Series E-ISSN: 1862-9121
Edition Number: 1
Number of Pages: XIV, 284
Number of Illustrations: 1 illustrations in colour
Topics: Mathematical Logic and Foundations, Probability Theory and Stochastic Processes