Perron-Frobenius theorem, large deviations, and random perturbations in random environments.
Perturbed Bessel processes
Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique
The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value for which the total variation norm between and π stays very close to 1 for , and falls rapidly to a value close to 0 for with a fall-off phase much shorter than . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...
Piecewise Markov processes in discrete time and their certain extensions
Pointwise ergodic theorems with rate and application to the CLT for Markov chains
Let T be Dunford–Schwartz operator on a probability space (Ω, μ). For f∈Lp(μ), p>1, we obtain growth conditions on ‖∑k=1nTkf‖p which imply that (1/n1/p)∑k=1nTkf→0 μ-a.e. In the particular case that p=2 and T is the isometry induced by a probability preserving transformation we get better results than in the general case; these are used to obtain a quenched central limit theorem for additive functionals of stationary ergodic Markov chains, which improves those of Derriennic–Lin and Wu–Woodroofe....
Pricing exotic options under a high-order Markovian regime switching model.
Probabilistic cellular automata and random fields with i.i.d. directions
Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is , and all the cells evolve synchronously. The new content of a cell is randomly chosen, independently of the others, according to a distribution depending only on the content of the cell itself and of its right neighbor. There are necessary and sufficient conditions on the four parameters of such a PCA to have a Bernoulli product invariant measure....
Problèmes à frontière libre et arbres de mesures
Propriété asymptotique d’un modèle statistique pour une chaîne de Markov à valeurs dans