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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...

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