Large deviation principles for Markov processes via phi-Sobolev inequalities.
Large deviation probabilities for random walks with semiexponential distributions.
Large deviation probabilities for some rescaled superprocesses
Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences
To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov...
Large deviations and isoperimetry over convex probability measures with heavy tails.
Large deviations and Nelson processes.
Large deviations and quasi-potential of a Fleming-Viot process.
Large deviations and stochastic calculus for large random matrices.
Large deviations and strong mixing
Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is also...
Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive Gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is...
Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes.
Large deviations, central limit theorems and convergence for Young measures and stochastic homogenizations
Large deviations, central limit theorems and Lp convergence for Young measures and stochastic homogenizations
We study the stochastic homogenization processes considered by Baldi (1988) and by Facchinetti and Russo (1983). We precise the speed of convergence towards the homogenized state by proving the following results: (i) a large deviations principle holds for the Young measures; if the Young measures are evaluated on a given function, then (ii) the speed of convergence is bounded in every Lp norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these results...
Large deviations for a random walk in dynamical random environment
Large deviations for a triangular array of exchangeable random variables
Large deviations for directed percolation on a thin rectangle
Following the recent investigations of Baik and Suidan in [Int. Math. Res. Not. (2005) 325–337] and Bodineau and Martin in [Electron. Commun. Probab. 10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ+2 whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, Int. Math. Res. Not. (2005) 325–337] and [T. Bodineau...
Large deviations for directed percolation on a thin rectangle
Following the recent investigations of Baik and Suidan in [Int. Math. Res. Not. (2005) 325–337] and Bodineau and Martin in [Electron. Commun. Probab. 10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ+2 whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, Int. Math. Res. Not. (2005) 325–337] and [T. Bodineau...
Large deviations for Dirichlet processes and Poisson-Dirichlet distribution with two parameters.
Large deviations for exchangeable observations with applications.