Recent Developments in Infinite-Dimensional Analysis and Quantum Probability: Papers in Honour of Takeyuki Hida’s 70th Birthday

This text is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles, it is a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important developments in contemporary white noise analysis and some of its applications. For this reason, not only the 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.

Table of Contents:
A White-Noise Approach to Stochastic Calculus.- Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility.- Infinite-Dimensional Analysis and Analytic Number Theory.- Bell Numbers, Log-Concavity, and Log-Convexity.- Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis.- Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation.- Ornstein-Uhlenbeck Path Integral and Its Application.- Remarks on a Noncanonical Representation for a Stationary Gaussian Process.- A White Noise Approach to Stochastic Neumann Boundary-Value Problems.- Quantum Cable Equations in Terms of Generalized Operators.- Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory.- Generalized Functions in Signal Theory.- Ergodic Properties of Random Positive Semigroups.- Wiener-Itô Theorem in Terms of Wick Tensors.- Donsker’s Delta Function of Lévy Process.- Approximation of Hunt Processes by Multivariate Poisson Processes.- Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors.- One Loop Approximation of the Chern-Simons Integral.- Quantum Mechanics and Brownian Motions.- Complex White Noise and Coherent State Representations.- Complexity in Dynamics and Computation.- On the Theory of KM20-Langevin Equations for Stationary Flows (2): Construction Theorem.- Vector Bundle-Valued Poisson and Cauchy Kernel Functions on Classical Domains.- On Differential Operators in White Noise Analysis.- Stochastic Differentiation — A Generalized Approach.- A Stochastic Process Generated by the Lévy Laplacian.- Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions.- Semigroup Domination on a Riemannian Manifold with Boundary.- TheProduct of Independent Random Variables with Regularly Varying Tails.- Entropy in Subordination and Filtering.- Asymptotic Windings of Brownian Motion Paths on Riemann Surfaces.