On small deviations of stationary Gaussian processes and related analytic inequalities

Michel J. G. Weber

Let $\{X_j,j\in \mathbb{Z}\}$ be a Gaussian stationary sequence having a spectral function $F$ of infinite type. Then for all $n$ and $z\ge 0$,$$ ¶\Big\{\sup_{j=1}^n |X_j|\le z \Big\}\le…