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Stochastic areas, winding numbers and Hopf fibrations

Stochastic areas, winding numbers and Hopf fibrations We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces $$\mathbb {CP}^n$$ CP n and $$\mathbb {CH}^n$$ CH n . 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 $$\mathbb {CP}^n$$ CP n the geometry of the Hopf fibration plays a central role, whereas for $$\mathbb {CH}^n$$ CH n it is the anti-de Sitter fibration. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Probability Theory and Related Fields Springer Journals

Stochastic areas, winding numbers and Hopf fibrations

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Probability Theory and Stochastic Processes; Theoretical, Mathematical and Computational Physics; Quantitative Finance; Mathematical and Computational Biology; Statistics for Business/Economics/Mathematical Finance/Insurance; Operations Research/Decision Theory
ISSN
0178-8051
eISSN
1432-2064
DOI
10.1007/s00440-016-0745-x
Publisher site
See Article on Publisher Site

Abstract

We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces $$\mathbb {CP}^n$$ CP n and $$\mathbb {CH}^n$$ CH n . 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 $$\mathbb {CP}^n$$ CP n the geometry of the Hopf fibration plays a central role, whereas for $$\mathbb {CH}^n$$ CH n it is the anti-de Sitter fibration.

Journal

Probability Theory and Related FieldsSpringer Journals

Published: Oct 21, 2016

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