Quaternionic Brownian Windings

Fabrice Baudoin; Nizar Demni; Jing Wang

doi:10.1007/s10959-020-01034-9

Quaternionic Brownian Windings

Fabrice Baudoin, Nizar Demni, Jing Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymptotic laws of these windings are shown to be Gaussian for the flat and spherical geometries while the hyperbolic winding exhibits a different long time-behavior. The corresponding asymptotic law seems to be new and is related to the Cauchy relativistic distribution.

Original language	English (US)
Pages (from-to)	2368-2385
Number of pages	18
Journal	Journal of Theoretical Probability
Volume	34
Issue number	4
DOIs	https://doi.org/10.1007/s10959-020-01034-9
State	Published - Dec 2021

Keywords

Cauchy relativistic distribution
Large time asymptotic
Quaternionic hyperbolic space
Quaternionic projective space
Stochastic winding

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1007/s10959-020-01034-9

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abstract = "We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymptotic laws of these windings are shown to be Gaussian for the flat and spherical geometries while the hyperbolic winding exhibits a different long time-behavior. The corresponding asymptotic law seems to be new and is related to the Cauchy relativistic distribution.",

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AU - Demni, Nizar

AU - Wang, Jing

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AB - We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymptotic laws of these windings are shown to be Gaussian for the flat and spherical geometries while the hyperbolic winding exhibits a different long time-behavior. The corresponding asymptotic law seems to be new and is related to the Cauchy relativistic distribution.

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KW - Quaternionic hyperbolic space

KW - Quaternionic projective space

KW - Stochastic winding

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Quaternionic Brownian Windings

Abstract

Keywords

ASJC Scopus subject areas

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