# Stochastic areas, winding numbers and Hopf fibrations

@article{Baudoin2016StochasticAW,
title={Stochastic areas, winding numbers and Hopf fibrations},
author={Fabrice Baudoin and Jing Wang},
journal={Probability Theory and Related Fields},
year={2016},
volume={169},
pages={977-1005}
}
• Published 20 February 2016
• Mathematics
• Probability Theory and Related Fields
We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces $$\mathbb {CP}^n$$CPn and $$\mathbb {CH}^n$$CHn. The characteristic functions of those processes are computed and limit theorems are obtained. In the case $$n=1$$n=1, we also study windings of the Brownian motion on those spaces and compute the limit distributions. For $$\mathbb {CP}^n$$CPn the geometry of the Hopf fibration plays a central role, whereas for $$\mathbb {CH}^n$$CHn it…
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