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

Recent Developments in Infinite-Dimensional Analysis and QuantumProbability 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.

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Content:
Front Matter....Pages i-1
A White-Noise Approach to Stochastic Calculus....Pages 3-25
Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility....Pages 27-40
Infinite-Dimensional Analysis and Analytic Number Theory....Pages 41-78
Bell Numbers, Log-Concavity, and Log-Convexity....Pages 79-87
Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis....Pages 89-100
Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation....Pages 101-117
Ornstein-Uhlenbeck Path Integral and Its Application....Pages 119-135
Remarks on a Noncanonical Representation for a Stationary Gaussian Process....Pages 137-139
A White Noise Approach to Stochastic Neumann Boundary-Value Problems....Pages 141-150
Quantum Cable Equations in Terms of Generalized Operators....Pages 151-164
Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory....Pages 165-174
Generalized Functions in Signal Theory....Pages 175-184
Ergodic Properties of Random Positive Semigroups....Pages 185-201
Wiener-It? Theorem in Terms of Wick Tensors....Pages 203-218
Donsker’s Delta Function of L?vy Process....Pages 219-231
Approximation of Hunt Processes by Multivariate Poisson Processes....Pages 233-243
Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors....Pages 245-252
One Loop Approximation of the Chern-Simons Integral....Pages 253-273
Quantum Mechanics and Brownian Motions....Pages 275-282
Complex White Noise and Coherent State Representations....Pages 283-291
Complexity in Dynamics and Computation....Pages 293-306
On the Theory of KM2O-Langevin Equations for Stationary Flows (2): Construction Theorem....Pages 307-322
Vector Bundle-Valued Poisson and Cauchy Kernel Functions on Classical Domains....Pages 323-332
On Differential Operators in White Noise Analysis....Pages 333-347
Stochastic Differentiation — A Generalized Approach....Pages 349-361
A Stochastic Process Generated by the L?vy Laplacian....Pages 363-373
Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions....Pages 375-384
Semigroup Domination on a Riemannian Manifold with Boundary....Pages 385-410
The Product of Independent Random Variables with Regularly Varying Tails....Pages 411-432
Entropy in Subordination and Filtering....Pages 433-439
Asymptotic Windings of Brownian Motion Paths on Riemann Surfaces....Pages 441-464

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Content:
Front Matter....Pages i-1
A White-Noise Approach to Stochastic Calculus....Pages 3-25
Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility....Pages 27-40
Infinite-Dimensional Analysis and Analytic Number Theory....Pages 41-78
Bell Numbers, Log-Concavity, and Log-Convexity....Pages 79-87
Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis....Pages 89-100
Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation....Pages 101-117
Ornstein-Uhlenbeck Path Integral and Its Application....Pages 119-135
Remarks on a Noncanonical Representation for a Stationary Gaussian Process....Pages 137-139
A White Noise Approach to Stochastic Neumann Boundary-Value Problems....Pages 141-150
Quantum Cable Equations in Terms of Generalized Operators....Pages 151-164
Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory....Pages 165-174
Generalized Functions in Signal Theory....Pages 175-184
Ergodic Properties of Random Positive Semigroups....Pages 185-201
Wiener-It? Theorem in Terms of Wick Tensors....Pages 203-218
Donsker’s Delta Function of L?vy Process....Pages 219-231
Approximation of Hunt Processes by Multivariate Poisson Processes....Pages 233-243
Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors....Pages 245-252
One Loop Approximation of the Chern-Simons Integral....Pages 253-273
Quantum Mechanics and Brownian Motions....Pages 275-282
Complex White Noise and Coherent State Representations....Pages 283-291
Complexity in Dynamics and Computation....Pages 293-306
On the Theory of KM2O-Langevin Equations for Stationary Flows (2): Construction Theorem....Pages 307-322
Vector Bundle-Valued Poisson and Cauchy Kernel Functions on Classical Domains....Pages 323-332
On Differential Operators in White Noise Analysis....Pages 333-347
Stochastic Differentiation — A Generalized Approach....Pages 349-361
A Stochastic Process Generated by the L?vy Laplacian....Pages 363-373
Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions....Pages 375-384
Semigroup Domination on a Riemannian Manifold with Boundary....Pages 385-410
The Product of Independent Random Variables with Regularly Varying Tails....Pages 411-432
Entropy in Subordination and Filtering....Pages 433-439
Asymptotic Windings of Brownian Motion Paths on Riemann Surfaces....Pages 441-464
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