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Article Dans Une Revue Stochastic Processes and their Applications Année : 2021

Quaternionic stochastic areas

Résumé

We study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces $\mathbb{H}H^n$ and $\mathbb{H}P^n$. The characteristic functions of fixed-time marginals of these processes are computed and allows 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 $\mathbb{H}H^n$, the geometry of the quaternionic anti-de Sitter fibration plays a central role , whereas for $\mathbb{H}P^n$, this role is played by the quaternionic Hopf fibration.

Dates et versions

hal-02372405 , version 1 (20-11-2019)

Identifiants

Citer

Fabrice Baudoin, Nizar Demni, Jing Wang. Quaternionic stochastic areas. Stochastic Processes and their Applications, 2021, 131, pp.311-339. ⟨10.1016/j.spa.2020.09.002⟩. ⟨hal-02372405⟩
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