Filtered random variables, bialgebras, and convolutions

DOI10.1063/1.1412465zbMath1019.81029arXivmath/0103034OpenAlexW2029814604MaRDI QIDQ2774776

Romuald Lenczewski

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103034

zbMATH Keywords

random walkscoproductconvolutionsGNS representationsmultiple symmetric Fock spacepolynomials in noncommuting variables

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Quantum stochastic calculus (81S25) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

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Cites Work

• Quantum Ito's formula and stochastic evolutions
• Unification of Fermion and Boson stochastic calculus
• Quantum independent increment processes on superalgebras
• A new example of `independence' and `white noise'
• Stochastic integration on the Cuntz algebra \({\mathcal O}_ \infty\)
• Quantum mechanical Wiener processes
• Direct sums of tensor products and non-commutative independence
• A q-analog of the quantum central limit theorem for SUq(2)
• Unification of Independence in Quantum Probability
• ADDITION OF INDEPENDENT VARIABLES IN QUANTUM GROUPS
• FILTERED STOCHASTIC CALCULUS
• Quantum random walk for U q(su(2)) and a new example of quantum noise

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