Quaternionic Brownian Windings

Fabrice Baudoin (), Nizar Demni () and Jing Wang ()
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Fabrice Baudoin: University of Connecticut
Nizar Demni: IRMAR, Université de Rennes 1
Jing Wang: Purdue University

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 2368-2385

Abstract: 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.

Keywords: Stochastic winding; Large time asymptotic; Quaternionic projective space; Quaternionic hyperbolic space; Cauchy relativistic distribution; 58J65; 53C26; 60J60 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01034-9

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