Moderate deviations of suprema of Gaussian processes A cyclic approximation criterion

We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X_x(t),t\in T_x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation theorem. We introduce a modulable diophantine approximation. Finally we study for general non-vanishing coefficient sequences, the behavior along lattices of almost periodic Gaussian polynomials with linearly independent frequencies, and use a lattice localized version of Kronecker’s theorem.