Festschrift Masatoshi Fukushima : in honor of Masatoshi Fukushima's Sanju /

Festschrift Masatoshi Fukushima : in honor of Masatoshi Fukushima's Sanju /

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Bibliographic Details
Other Authors: Fukushima, Masatoshi, 1935-, Chen, Zhen-Qing, Jacob, Niels, Takeda, Masayoshi, Uemura, Toshihiro
Format: Electronic eBook
Language:English
Published: New Jersey : World Scientific, 2014.
Series:Interdisciplinary mathematical sciences ; volume 17
Subjects:
Mathematical analysis.
Stochastic analysis.
Probabilities.
Festschriften
Festschriften.
Online Access:CONNECT
Table of Contents:
  • Contents
  • Preface
  • Professor Fukushima's Work
  • 1. The mathematical work of Masatoshi Fukushima
  • An Essay
  • References
  • Further References
  • 2. Bibliography of Masatoshi Fukushima
  • Expository Writing
  • Seminar on Probability (in Japanese)
  • Monographs and Textbooks
  • Contributions
  • 3. Quasi regular Dirichlet forms and the stochastic quantization problem
  • 1. Introduction
  • 2. Symmetric quasi regular Dirichlet forms
  • 3. Classical Dirichlet forms on Banach spaces and weak solutions to SDE
  • 4. Applications to stochastic quantization in finite and infinite volume4.1. Finite volume
  • 4.2. Infinite volume
  • 4.3. Ergodicity
  • 4.4. Additional remarks
  • 5. Further developments
  • 6. Acknowledgements
  • References
  • 4. Comparison of quenched and annealed invariance principles for random conductance model: Part II
  • 1. Introduction
  • 2. Description of the environment
  • 3. Preliminary results
  • 4. Estimates on the process Xn,2
  • 5. Acknowledgements
  • References
  • 5. Some historical aspects of error calculus by Dirichlet forms
  • 1. Introduction2. Gauss inventor of the carre du champ operator?
  • 3. Why should we ask the quadratic form to be closed?
  • 4. Dirichlet form generated by an approximation
  • 5. Small errors what does it mean?
  • 6. Trails of research
  • References
  • 6. Stein's method, Malliavin calculus, Dirichlet forms and the fourth moment theorem
  • 1. Introduction
  • 2. Stein's method
  • 2.1. How it began
  • 2.2. A general framework
  • 2.3. Normal approximation
  • 3. Malliavin calculus
  • 3.1. A brief history
  • 3.2. Malliavin derivatives
  • 3.3. Wiener chaos and multiple integrals3.4. Main properties of Malliavin operators
  • 4. Connecting Stein's method with Malliavin calculus
  • 5. The Nualart-Peccati criterion of the fourth moment and Ledoux's idea
  • 5.1. Some history
  • 5.2. Overview of the proof of Nourdin and Peccati
  • 5.3. About Ledoux's generalization
  • 6. The general fourth moment Theorem for Dirichlet forms
  • 6.1. The Dirichlet structures
  • 6.2. Fourth moment theorem for Dirichlet structures with (H1) and (H2)
  • 6.3. Dirichlet structures with (H1) and (H2)
  • 7. Acknowledgments

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