Lévy processes that can creep downwards never increase
Let 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 have smooth densities.
The L-decomposable and the bi-decomposable models are two families of distributions on the set of all permutations of the first 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...
We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on . We mainly investigate subordinated semigroups in the Bochner sense by means of -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.
Let be a nonnegative function with its only singularity at , e.g. , . We study the behavior of the Wiener process in left and right hand neighborhoods of level crossings by finding necessary and sufficient conditions on for the integrals of to be finite or infinite.