Thermodynamic Formalism and Large Deviation Principle of Multiplicative Ising Models

Thermodynamic Formalism, Large Deviation, and Multifractals

Large Deviation Principle and Inviscid Shell Models

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...

Large Deviation Principle for General Occupancy Models

We use process level large deviation analysis to obtain the rate function for a general family of occupancy problems. Our interest is the asymptotics of the empirical distributions of various quantities (such as the fraction of urns that contain a given number of balls). In the general setting, balls are allowed to land in a given urn depending on the urn’s contents prior to the throw. We discu...

A large deviation principle for Dirichlet posteriors

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...

Large deviation principle for enhanced Gaussian processes

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...