THE QUANTUM DECOMPOSITION OF RANDOM VARIABLES WITHOUT MOMENTS

DOI10.1142/S0219025713500124zbMath1283.60107OpenAlexW2088788045MaRDI QIDQ2842032

Habib Rebei, Anis Riahi, Luigi Accardi

Publication date: 30 July 2013

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025713500124

zbMATH Keywords

Lévy processesFock spacesKolmogorov decompositionpositive definite kernelinfinitely divisible lawquantum decompositionAraki-Woods-Parthasarathy-Schmidt theoremgeneralized field operator

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Brownian motion (60J65) Probabilistic potential theory (60J45) White noise theory (60H40) Renormalization group methods applied to problems in quantum field theory (81T17) Quantum stochastic calculus (81S25)

Related Items (3)

On the one-mode quadratic Weyl operators ⋮ On the Bogolyubov endomorphisms of the renormalized square of white noise algebra ⋮ Noncommutative quantum decomposition of Gegenbauer white noise process

Cites Work

• Analysis of generalized Lévy white noise functionals
• Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
• WHITE NOISE LÉVY–MEIXNER PROCESSES THROUGH A TRANSFER PRINCIPAL FROM ONE-MODE TO ONE-MODE TYPE INTERACTING FOCK SPACES
• Interacting Fock Spaces and Gaussianization of Probability Measures
• Representations of the Schrödinger algebra and Appell systems
• Donsker's delta function of Lévy process

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