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Title: Quaternionic Brownian Windings
We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymp- totic 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.  more » « less
Award ID(s):
1901315 1855523
PAR ID:
10221362
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Theoretical Probability
ISSN:
0894-9840
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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