Gaussian approximation for residuals of stationary autoregressive process in Hölder norm

The paper treats the hölderian approximation for partial sums process of stationary autoregressive residuals (AR(p), $p \geq 1$). We consider the polygonal smoothed process of these partial sums and we prove the Hölder convergence of this sequence of processes to the Brownian motion for any order $\alpha<\frac{1}{2}$. A statistical application of this convergence to detect epidemic change and simulation results are also presented.