Théorème ergodique ponctuel pour les suites uniformes
Vitesse de convergence vers l'état d'équilibre pour des dynamiques markoviennes non höldériennes
Transfer operator for piecewise affine approximations of interval maps
Invariant measures for piecewise convex transformations of an interval
We investigate the existence and ergodic properties of absolutely continuous invariant measures for a class of piecewise monotone and convex self-maps of the unit interval. Our assumption entails a type of average convexity which strictly generalizes the case of individual branches being convex, as investigated by Lasota and Yorke (1982). Along with existence, we identify tractable conditions for the invariant measure to be unique and such that the system has exponential decay of correlations on...
Pressure and recurrence
We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) , where is the element of the partition containing and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).
Exponential inequalities for VLMC empirical trees
A seminal paper by Rissanen, published in 1983, introduced the class of Variable Length Markov Chains and the algorithm Context which estimates the probabilistic tree generating the chain. Even if the subject was recently considered in several papers, the central question of the rate of convergence of the algorithm remained open. This is the question we address here. We provide an exponential upper bound for the probability of incorrect estimation of the probabilistic tree, as a function...
Page 1