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Affine Dunkl processes of type A ˜ 1

François Chapon (2012)

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

We introduce the analogue of Dunkl processes in the case of an affine root system of type A ˜ 1 . The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is given by a Gaussian process on the ultraspherical hypergroup [ 0 , 1 ] . We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and give a martingale...

Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic

Mamadou Moustapha Mbaye (2016)

Nonautonomous Dynamical Systems

In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S2−almost automorphic) processes in distribution. We establish some interesting results on the functional space of such processes like an composition theorems. Next, under some suitable assumptions, we establish the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise in case...

Almost Everywhere Convergence of Riesz-Raikov Series

Ai Fan (1995)

Colloquium Mathematicae

Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series ∑ n = 1 ∞ c n f ( T n x ) converges almost everywhere with respect to Lebesgue measure provided that ∑ n = 1 ∞ | c n | 2 l o g 2 n < ∞ .

Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier

Troels Roussau Johansen (2011)

Studia Mathematica

The maximal operator S⁎ for the spherical summation operator (or disc multiplier) S R associated with the Jacobi transform through the defining relation S R f ^ ( λ ) = 1 | λ | ≤ R f ̂ ( t ) for a function f on ℝ is shown to be bounded from L p ( ℝ ₊ , d μ ) into L p ( ℝ , d μ ) + L ² ( ℝ , d μ ) for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from L p ₀ , 1 ( ℝ ₊ , d μ ) into L p ₀ , ∞ ( ℝ , d μ ) + L ² ( ℝ , d μ ) . In particular S R f ( t ) R > 0 converges almost everywhere towards f, for f ∈ L p ( ℝ ₊ , d μ ) , whenever (4α + 4)/(2α + 3) < p ≤ 2.

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