Notes on spherical bifractional Brownian motion
Volume 9, Issue 3 (2022), pp. 339–355
Pub. online: 7 June 2022
Type: Research Article
Open Access
Open Access
Received
30 September 2021
30 September 2021
Revised
3 March 2022
3 March 2022
Accepted
17 May 2022
17 May 2022
Published
7 June 2022
7 June 2022
Abstract
The existence of the bifractional Brownian motion ${B_{H,K}}$ indexed by a sphere when $K\in (-\infty ,1]\setminus \{0\}$ and $H\in (0,1/2]$ is discussed, and the asymptotics of its excursion probability $\mathbb{P}\left\{{\sup _{M\in \mathbb{S}}}{B_{H,K}}(M)>x\right\}$ as $x\to \infty $ is studied.
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