We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their...

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law...

For the Ornstein–Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding this trichotomy, we investigate sharp large deviation principles for this estimator in the...