Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

1. Front Matter

   Pages i-1

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2. A White-Noise Approach to Stochastic Calculus

   • Luigi Accardi, Yun Gang Lu, Igor V. Volovich

   Pages 3-25

3. Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility

   • Sergio Albeverio, Alexei Daletskii, Yuri Kondratiev, Michael Röckner

   Pages 27-40

4. Infinite-Dimensional Analysis and Analytic Number Theory

   • Asao Arai

   Pages 41-78

5. Bell Numbers, Log-Concavity, and Log-Convexity

   • Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

   Pages 79-87

6. Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis

   • Dong Myung Chung, Un Cig Ji

   Pages 89-100

7. Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation

   • Isamu Dôku

   Pages 101-117

8. Ornstein-Uhlenbeck Path Integral and Its Application

   • Hiroshi Ezawa

   Pages 119-135

9. Remarks on a Noncanonical Representation for a Stationary Gaussian Process

   • Yuji Hibino, Masuyuki Hitsuda, Hiroshi Muraoka

   Pages 137-139

10. A White Noise Approach to Stochastic Neumann Boundary-Value Problems

    • Helge Holden, Bernt Øksendal

    Pages 141-150

11. Quantum Cable Equations in Terms of Generalized Operators

    • Zhiyuan Huang, Caishi Wang, Xiangjun Wang

    Pages 151-164

12. Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory

    • Shunsuke Ihara

    Pages 165-174

13. Generalized Functions in Signal Theory

    • Friedrich Jondral

    Pages 175-184

14. Ergodic Properties of Random Positive Semigroups

    • Hiroshi Kunita

    Pages 185-201

15. Wiener-Itô Theorem in Terms of Wick Tensors

    • H. -H. Kuo, Y. -J. Lee, C. -Y. Shih

    Pages 203-218

16. Donsker’s Delta Function of Lévy Process

    • Yuh-Jia Lee, Hsin-Hung Shih

    Pages 219-231

17. Approximation of Hunt Processes by Multivariate Poisson Processes

    • Zhi-Ming Ma, Michael Röckner, Wei Sun

    Pages 233-243

18. Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors

    • Pranab K. Mandal, V. Mandrekar

    Pages 245-252

19. One Loop Approximation of the Chern-Simons Integral

    • Itaru Mitoma

    Pages 253-273

20. Quantum Mechanics and Brownian Motions

    • Mikio Namiki

    Pages 275-282

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included.
The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

• Finite
• Manifold
• Random variable
• Variable
• calculus
• equation
• function
• geometry
• statistics
• theorem

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