Let Xk be a sequence of independent and identically distributed random variables taking values in a compact metric space Ω, and consider the problem of estimating the law of X1 in a Bayesian framework. A conjugate family of priors for non-parametric Bayesian inference is the Dirichlet process priors popularized by Ferguson. We prove that if the prior distribution is Dirichlet, then the sequence...

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N . We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölderor modulus topology, appears as special case. © 2007 Elsevier Masson SAS. All rights reserved. Résumé Nous etudions les princ...

In this paper, we present a large deviation principle for partial sums processes indexed by the half line, which is particularly suited to queueing applications. The large deviation principle is established in a topology that is finer than the topology of uniform convergence on compacts and in which the queueing map is continuous. Consequently, a large deviation principle for steady-state queue...

A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient ν converges to 0 and the noise intensity is multiplied by ν , we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in ([0, T],V ) for the topology of uniform convergence on [0, T], but where V is endowed with a topolog...