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Median for metric spaces

Nacereddine Belili, Henri Heinich (2001)

Applicationes Mathematicae

We consider a Köthe space ( , | | · | | ) of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that | | d ( X , Y ) | | | | d ( X , Z ) | | for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications....

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...

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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