RESEARCH

We extend Naseri Sadr’s table theorem from continuous real-valued functions to continuous sections of real line bundles with arbitrary connections over closed connected Riemannian surfaces of odd Euler characteristic. The proof computes the top Stiefel–Whitney class of a rank-three real vector bundle over a closed three-manifold. As applications, we obtain the spherical table theorem for odd functions and give an alternative proof of the known theorem for even functions.

Let \((\bar{X}_t)_{t\in\mathbb{R}}\) be the stationary solution for an additive stochastic differential equation driven by a fractional Brownian motion. We give an upper bound for a joint fourth cumulant of the form \(\kappa_4(f_0(\bar{X}_0), f_1(\bar{X}_{t_1}), f_2(\bar{X}_{t_2}), f_3(\bar{X}_{t_3}))\). Our tool is the partial Malliavin calculus for the stationary solution for an SDE driven by fBM. As an application, we show that local asymptotic normality of a likelihood ratio field for the drift parameter of a fractional SDE holds even in the case \(0 < H \leq 1/4\).