ELLIPTIC GAUSSIAN RANDOM-PROCESSES

We study the Gaussian random fields indexed by R-d whose covariance is defined in all generality as the parametrix of an elliptic pseudo-dif ferential operator with minimal regularity asumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposi tion of the field on this corresponding basis yields its iterated loga rithm law and its uniform modulus of continuity. We also characterize the local scalings of the field in term of the properties of the princ ipal symbol of the pseudodifferential operator. Similar results are ob tained for the Multi-Fractional Brownian Motion.