Results 91 to 100 of about 108 (105)

The Ornstein–Uhlenbeck Operator and the Ornstein–Uhlenbeck Semigroup

2019
In this chapter we are going to define and study the Ornstein–Uhlenbeck operator and the Ornstein–Uhlenbeck semigroup. They are analogous, in the Gaussian harmonic analysis, to the Laplacian and the heat semigroup in the classical case. Then, we study an important property of the Ornstein–Uhlenbeck semigroup, the hypercontractivity property, and some ...
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QUANTUM FRACTIONAL ORNSTEIN–UHLENBECK SEMIGROUPS AND ASSOCIATED POTENTIALS

Rocky Mountain Journal of Mathematics
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Ettaieb, Aymen, Missaoui, Sonia, Rguigui, Hafedh   +2 more
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L ¹ ‐SMOOTHING FOR THE ORNSTEIN–UHLENBECK SEMIGROUP

Mathematika, 2012
Given a probability density, we estimate the rate of decay of the measure of the level sets of its evolutes by the Ornstein–Uhlenbeck semigroup. The rate is faster than what follows from the preservation of mass and Markov’s inequality.
Ball, K., Barthe, Franck, Bednorz, W., Oleszkiewicz, Krzysztof, Wolff, P.   +4 more
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Positivity of Perturbed Ornstein-Uhlenbeck Semigroups on Cb(H)

Semigroup Forum, 2005
The authors develop the abstract theory of bi-continuous semigroups. The bi-continuous semigroups are semigroups of linear operators in a Banach space, where the usual conditions of strong continuity with respect to the basic topology are replaced with strong continuity with respect to a certain locally convex topology which is weaker than the basic ...
Es-Sarhir, Abdelhadi, Farkas, Bálint
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On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions

Archiv der Mathematik, 2007
We extend to infinite dimensions an explicit formula of Chill, Fasangová, Metafune, and Pallara for the optimal angle of analyticity of analytic Ornstein-Uhlenbeck semigroups. The main ingredient is an abstract representation of the Ornstein-Uhlenbeck operator in divergence form.
Maas, J. (author), Van Neerven, J.M.A.M. (author)   +1 more
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Psi-entropy inequalities for the Ornstein-Uhlenbeck semigroup

Semigroup Forum, 2012
Let \(P_t\) be the Ornstein-Uhlenbeck semigroup and let \(\gamma\) be the standard Gaussian measure on \(\mathbb R^n\). For a strictly convex smooth function \(\psi\) on \((0,\infty)\) such that \(\psi(0^+)=0\) and so that \(\frac{1}{\psi''}\) is concave, let \[ \text{Ent}_t^\psi(f)= \gamma(\psi(f))- \gamma(\psi(P_tf)),\;\;t>0,\;\;f\geq 0.
Bentaleb, Abdellatif, Fahlaoui, Saïd, Hafidi, Ali   +2 more
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Bounded Perturbations of Ornstein-Uhlenbeck Semigroups

2002
Let H be a separable Hilbert space (norm ∣ · ∣, inner product (·, ·)) and L(H) the Banach algebra of all linear bounded operators from H into H endowed with the norm. $$ \left\| T \right\| = \sup \{ \left| {Tx} \right|,x \in H,\left| x \right| \leqslant 1\} . $$
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Multiparameter Processes Associated with Ornstein-Uhlenbeck Semigroups

1994
We consider Sobolev spaces and capacities associated with a generalized Ornstein-Uhlenbeck semigroup. In order to obtain a probabilistic counterpart, we construct and investigate certain multiparameter processes. These are used to characterize polar sets and quasi-continuous functions.
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Non Gradient Perturbations of Ornstein-Uhlenbeck Semigroups

1999
We are concerned with the following linear operator N in a separable Hubert space i7, (1.1)
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Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces

Stochastic Analysis and Applications, 1998
We prove hypercontractivity of nonsymmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, using direct probabilistic arguments. Our results imply exponential convergence at infinity for the semigroup.
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