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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.
We analyze a stochastic neuronal network model which corresponds to an all-to-all network
of discretized integrate-and-fire neurons where the synapses are failure-prone. This
network exhibits different phases of behavior corresponding to synchrony and asynchrony,
and we show that this is due to the limiting mean-field system possessing multiple
attractors. We also show that this mean-field limit exhibits a first-order phase
transition as a function...
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...
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