Maximum Likelihood Estimator for Hidden Markov Models in continuous time

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions of the chain.Comment: Warning: due to a flaw in the publishing process, some of the references in the published version of the article are confuse

Current large deviations in a driven dissipative model

We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where the energy is injected at the boundary and dissipated in the bulk. The large deviation functional for the particle currents flowing through the system is computed and some physical consequences are discussed: the mechanism for local current fluctuations, dynamical phase transitions, the fluctuation-relation