Sur La Regularite Des Fonctions Aleatoires D'Ornstein-Uhlenbeck A Valeurs Dans lp, p ∈ [ 1

In this note, we study the regularity of RN-valued random functions X - (Xn, n ∈ N) on R such that$X_n(t) = a_nx_n(b_nt),\quad t \in \mathbb{R}, n \in \mathbb{N},$where$\mathbf{a} = (a_n) \subset \mathbb{R}^+, \mathbf{b} = (b_n) \subset \mathbb{R}^+$and (xn, n ∈ N) is an i.i.d. sequence of gaussian centered stationary real random functions on R. If the common covariance of the xn's verifies some very weak regularity assumptions, then their paths are continuous in lp, p ∈ [ 1,∞[ if and only if they are in this space and some integral depending uniquely on p and on a and b is convergent. These results extend and refine some previous results concerning only the case p ∈ [ 2, ∞[.