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Minorantes harmoniques et potentiels - Localisation sur une famille de temps d'arrêt - Réduite forte

Hélène Airault (1974)

Annales de l'institut Fourier

X = ( X t , ζ , M t , E x ) est un processus de Markov sur un espace localement compact, et h est une fonction excessive. Soit T une famille de temps d’arrêt h est T -harmonique si pour tout x , E x [ h ( X t ) ] = h ( x ) pour tout temps d’arrêt τ appartenant à T . h est un T potentiel si sa plus grande minorante forte T -harmonique est nulle. La plus grande minorante forte T -harmonique de h est égale à la somme de deux fonctions excessives qui sont étudiées. On déduit différentes caractérisations des T -potentiels suivant les propriétés de la famille...

Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation

A. Genadot, M. Thieullen (2014)

ESAIM: Probability and Statistics

In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. Adv. Appl. Probab. 44 (2012) 749–773], the authors addressed the question of averaging for a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimensions. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuations of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated...

Multistage multivariate nested distance: An empirical analysis

Sebastiano Vitali (2018)

Kybernetika

Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and...

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