Notes on spherical bifractional Brownian motion

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.