Processus gaussiens, markoviens d'ordre p, fortement markoviens d'ordre p et problème de Dirichlet stochastique
Régularité des processus gaussiens elliptiques et le modèle hiérarchique
Elliptic self-similar stochastic processes.
Let M be a random measure and L be an elliptic pseudo-differential operator on Rd. We study the solution of the stochastic problem LX = M, X(O) = O when some homogeneity and integrability conditions are assumed. If M is a Gaussian measure the process X belongs to the class of Elliptic Gaussian Processes which has already been studied. Here the law of M is not necessarily Gaussian. We characterize the solutions X which are self-similar and with stationary increments in terms of the driving mcasure...
Hydrodynamical limit for the asymmetric zero-range process
Elliptic gaussian random processes.
We study the Gaussian random fields indexed by R whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol...
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