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Malliavin calculus for stable processes on homogeneous groups

Piotr Graczyk (1991)

Studia Mathematica

Let μ t t > 0 be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures μ t have smooth densities.

Markov bases of conditional independence models for permutations

Villő Csiszár (2009)

Kybernetika

The L-decomposable and the bi-decomposable models are two families of distributions on the set S n of all permutations of the first n positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by...

On exit laws for subordinated semigroups by means of 𝒞 1 -subordinators

Mohamed Hmissi, Ezzedine Mliki (2010)

Commentationes Mathematicae Universitatis Carolinae

We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on L 2 ( m ) . We mainly investigate subordinated semigroups in the Bochner sense by means of 𝒞 1 -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.

On the divergence of certain integrals of the Wiener process

Lawrence A. Shepp, John R. Klauder, Hiroshi Ezawa (1974)

Annales de l'institut Fourier

Let f ( x ) be a nonnegative function with its only singularity at x = 0 , e.g. f ( x ) = | x | - α , α > 0 . We study the behavior of the Wiener process W ( t ) in left and right hand neighborhoods of level crossings by finding necessary and sufficient conditions on f for the integrals of f ( W ( t ) ) to be finite or infinite.

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