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Stochastic Analysis: Classical and Quantum

WHITE NOISE CALCULUS AND STOCASTIC CALCULUS

Luigi Accardi, Andreas Boukas

Published Oct 1, 2005• 1 citation
Publisher

Abstract

In section (2), after recalling some basic points of \n the structure theory of classical stochastic process, we illustrate how \nquantum probability can substantiate Hida's vision about the "elementality" \nof white noise, i.e. that any other (purely non deterministic) process can be \nin some sense ``built'' from it.

DOI
10.1142/9789812701541_0020

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In section (2), after recalling some basic points of \n the structure theory of classical stochastic process, we illustrate how \nquantum probability can substantiate Hida's vision about the "elementality" \nof white noise, i.e. that any other (purely non deterministic) process can be \nin some sense ``built'' from it.
# Part 1: # White Noise Functional Approach to Polymer Entanglements (C C Bernido & M V Carpio-Bernido) # White Noise Analysis, Quantum Field Theory, and Topology (A Hahn) # A Topic on Noncanonical Representations of Gaussian Processes (Y Hibino) # Integral Representation of Hilbert-Schimdt Operators on Boson Fock Space (U C Ji) # The Dawn of White Noise Analysis (I Kubo) # White Noise Stochastic Integration (H-H Kuo) # Connes-Hida Calculus and Bismut-Quillen Superconnections (R Leandre & H Ouerdiane) # A Quantum Decomposition of Levy Processes (Y-J Lee & H-H Shih) # Generalized Entanglement and Its Classification (T Matsuoka) # A White Noise Approach to Fractional Brownian Motion (D Nualart) # Adaptive Dynamics in Quantum Information and Chaos (M Ohya) # Micro-Macro Duality in Quantum Physics (I Ojima) # White Noise Measures Associated to the Solutions of Stochastic Differential Equations (H Ouerdiane) # A Remark on Sets of Infinite Dimensional Spaces with Full or Zero Capacity (J Ren & M Rockner) # An Infinite Dimensional Laplacian in White Noise Theory (K Saito) # Invariance of Poisson Noise (Si Si et al.) # Nonequilibrium Steady States with Bose-Einstein Condensates (S Tasaki & T Matsui) # Multidimensional Skew Reflected Diffusions (G Trutnau) # On Quantum Mutual Type Entropies and Quantum Capacity (N Watanabe) # Part 2: # White Noise Calculus and Stochastic Calculus (L Accardi & A Boukas)