Quaternionic stochastic areas

Fabrice Baudoin, Nizar Demni and Jing Wang

Stochastic Processes and their Applications, 2021, vol. 131, issue C, 311-339

Abstract: We define and study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces HHn and HPn. The characteristic functions of fixed-time marginals of these processes are computed and allow for the explicit description of their corresponding large-time limits. We also obtain exact formulas for the semigroup densities of the stochastic area processes using a Doob transform in the former case and the semigroup density of the circular Jacobi process in the latter. For HHn, the geometry of the quaternionic anti-de Sitter fibration plays a central role, whereas for HPn, this role is played by the quaternionic Hopf fibration.

Keywords: Stochastic area process; Large time asymptotic behavior; Quaternionic Hopf fibration; Quaternionic anti-de Sitter fibration (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:131:y:2021:i:c:p:311-339

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DOI: 10.1016/j.spa.2020.09.002

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