Upper functions for $\mathbb{L}_{p}$-norms of Gaussian random fields

In this work, we derive explicit probability distribution functions for the random variables associated with the output of similarity functions computed on local windows of

In particular, there is a critical regime where the limit random field is operator-scaling and inherits the full dependence structure of the discrete model, whereas in other regimes

However, there is another approach to random processes that is more elementary, involving smooth random functions defined by finite Fourier series with random coefficients,

To be more precise, we aim at giving the explicit probability distribution function of the random variables associated to the output of similarity functions between local windows

Using the developed general technique, we derive uniform bounds on the L s -norms of empirical and regression-type processes.. Use- fulness of the obtained results is illustrated

In Section 3.1 we derive upper functions for L p -norm of some Wiener integrals (Theorem 1) and in Section 3.2 we study the local modulus of continuity of gaussian functions defined

In particular we prove that the random variables whose associated DDS martingale has bounded bracket can- not belong to a finite sum of Wiener chaoses and we relate our work to

L´evy’s construction of his “mouvement brownien fonction d’un point de la sph`ere de Riemann” in [11], we prove that to every square integrable bi-K-invariant function f : G → R