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On smoothing properties of transition semigroups associated to a class of SDEs with jumps

Seiichiro Kusuoka, Carlo Marinelli (2014)

Annales de l'I.H.P. Probabilités et statistiques

We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in ℝ d driven by additive pure-jump Lévy noise. In particular, we assume that the Lévy process driving the SDE is the sum of a subordinated Wiener process Y (i.e. Y = W ∘ T , where T is an increasing pure-jump Lévy process starting at zero and independent of the Wiener process W ) and of an arbitrary Lévy process independent of Y , that the drift coefficient is continuous (but not...

Singular measures and the key of G.

Stephen M. Buckley, Paul MacManus (2000)

Publicacions Matemàtiques

We construct a sequence of doubling measures, whose doubling constants tend to 1, all for which kill a Gδ set of full Lebesgue measure.

The Rényi distances of Gaussian measures

Jiří Michálek (1999)

Kybernetika

The author in the paper evaluates the Rényi distances between two Gaussian measures using properties of nuclear operators and expresses the formula for the asymptotic rate of the Rényi distances of stationary Gaussian measures by the corresponding spectral density functions in a general case.

Transformations preserving the Hausdorff-Besicovitch dimension

Sergio Albeverio, Mykola Pratsiovytyi, Grygoriy Torbin (2008)

Open Mathematics

Continuous transformations preserving the Hausdorff-Besicovitch dimension (“DP-transformations”) of every subset of R 1 resp. [0, 1] are studied. A class of distribution functions of random variables with independent s-adic digits is analyzed. Necessary and sufficient conditions for dimension preservation under functions which are distribution functions of random variables with independent s-adic digits are found. In particular, it is proven that any strictly increasing absolutely continuous distribution...

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