Dilation of a class of quantum dynamical semigroups with unbounded generators on UHF algebras
We create a general framework for describing domains of functions of power-bounded operators given by power series with log-convex coefficients. This sheds new light on recent results of Assani, Derriennic, Lin and others. In particular, we resolve an open problem regarding the "one-sided ergodic Hilbert transform" formulated in a 2001 paper by Derriennic and Lin.
We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.
Soit U une fonction définie sur un ensemble fini E muni d'un noyau markovien irréductible M. L'objectif du papier est de comparer théoriquement deux procédures stochastiques de minimisation globale de U : le recuit simulé et un algorithme génétique. Pour ceci on se placera dans la situation idéalisée d'une infinité de particules disponibles et nous ferons une hypothèse commode d'existence de suffisamment de symétries du cadre (E,M,U). On verra notamment que contrairement au recuit simulé, toute...