Hypergroups and Quantum Bessel Processes of Non-integer Dimensions

Wojciech Matysiak ()
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Wojciech Matysiak: Politechnika Warszawska

Journal of Theoretical Probability, 2017, vol. 30, issue 4, 1677-1691

Abstract: Abstract It is demonstrated how to use a certain family of commutative hypergroups to provide a universal construction of Biane’s quantum Bessel processes of all dimensions not smaller than 1. The classical Bessel processes $$\text {BES}(\delta )$$ BES ( δ ) are analogously constructed with the aid of the Bessel–Kingman hypergroups for all, not necessarily integer, dimensions $$\delta \ge 1$$ δ ≥ 1 .

Keywords: Quantum Bessel process; Bessel process; Hypergroup; Gelfand pair; Primary 60J25; Secondary 43A62 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0688-2

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