Some comments on quantum probability
Kalyanapuram Rangachari Parthasarathy (1989)
Séminaire de probabilités de Strasbourg
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Kalyanapuram Rangachari Parthasarathy (1989)
Séminaire de probabilités de Strasbourg
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Ruffing, Andreas (2000)
Discrete Dynamics in Nature and Society
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Shigeru Haruki (1984)
Annales Polonici Mathematici
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Wilhelm von Waldenfels (1990)
Séminaire de probabilités de Strasbourg
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Ruffing, Andreas (2000)
Discrete Dynamics in Nature and Society
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Shigeru Haruki (1977)
Annales Polonici Mathematici
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Harold Exton (1992)
Collectanea Mathematica
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K. Urbanik (1961)
Studia Mathematica
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Adam Osękowski (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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Assume that u, v are conjugate harmonic functions on the unit disc of ℂ, normalized so that u(0) = v(0) = 0. Let u*, |v|* stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate ℙ(|v|* ≥ 1)≤ (1 + 1/3² + 1/5² + 1/7² + ...)/(1 - 1/3² + 1/5² - 1/7² + ...) 𝔼u*. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions...
Philippe Jaming (2001)
Bollettino dell'Unione Matematica Italiana
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In questo articolo studieremo le relazioni fra le funzioni armoniche nella palla iperbolica (sia essa reale, complessa o quaternionica), le funzione armoniche euclidee in questa palla, e le funzione pluriarmoniche sotto certe condizioni di crescita. In particolare, estenderemo al caso quaternionico risultati anteriori dell'autore (nel caso reale), e di A. Bonami, J. Bruna e S. Grellier (nel caso complesso).
Katarzyna Lubnauer (2004)
Studia Mathematica
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A noncommutative analogue of limit theorems in classical probability theory for distributions of canonical pairs of observables is considered. A complete description of all limit probability operators which are quantum counterparts of the classical infinitely divisible and semistable laws is obtained in the case when scalar norming is generalised to norming by 2 × 2 matrices.
Kulinich, Grigori L., Kushnirenko, Svitlana V. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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