Hypergroups and Quantum Bessel Processes of Non-integer Dimensions
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🧮 math.PR
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besseldimensionshypergroupsprocessesdeltaquantumanalogouslybessel-kingman
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It is demonstrated how to use 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 BES$(\delta)$ are analogously constructed with the aid of the Bessel-Kingman hypergroups for all, not necessarily integer, dimensions $\delta\ge1$.
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