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Title Festschrift Masatoshi Fukushima : in honor of Masatoshi Fukushima's Sanju / edited by Zhen-Qing Chen (University of Washington, USA), Niels Jacob (Swansea University, UK), Masayoshi Takeda (Tohoku University, Japan), Toshihiro Uemura (Kansai University, Japan)
Published New Jersey : World Scientific, 2014

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Description 1 online resource
Series Interdisciplinary mathematical sciences ; volume 17
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
Bibliography Includes bibliographical references
Notes Print version record
Subject Mathematical analysis.
Stochastic analysis.
Probabilities.
Probability
probability.
MATHEMATICS -- Applied.
MATHEMATICS -- Probability & Statistics -- General.
Mathematical analysis
Probabilities
Stochastic analysis
Genre/Form Festschriften
Festschriften.
Form Electronic book
Author Fukushima, Masatoshi, 1935-
Chen, Zhen-Qing
Jacob, Niels
Takeda, Masayoshi
Uemura, Toshihiro
ISBN 9789814596534
9814596531