publication . Article . Other literature type . 1997

Noncommutative Brownian Motion in Monotone Fock Space

Muraki, Naofumi;
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  • Published: 01 Feb 1997 Journal: Communications in Mathematical Physics, volume 183, pages 557-570 (issn: 0010-3616, eissn: 1432-0916, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
An example of noncommutative Brownian motion is constructed on the monotone Fock space which is a kind of “Fock space” generated by all the decreasing finite sequences of positive real numbers. The probability distribution at time \(\) associated to this Brownian motion is shown to be the arcsine law normalized to mean 0 and variance t.
Subjects
arXiv: Mathematics::Probability
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Martingale representation theorem, Mathematics, Noncommutative geometry, Reflected Brownian motion, Mathematical analysis, Brownian excursion, Fractional Brownian motion, Heavy traffic approximation, Topology, Fock space, Diffusion process, 81S25, 46L50
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publication . Article . Other literature type . 1997

Noncommutative Brownian Motion in Monotone Fock Space

Muraki, Naofumi;