Results 91 to 100 of about 435 (135)

Stochastic Heat Equation with Ornstein-Uhlenbeck Operator

SSRN Electronic Journal, 2022
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Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators

Mediterranean Journal of Mathematics, 2010
In this paper, the authors discuss the hypercyclicity and supercyclicity of semigroups generated by Ornstein-Uhlenbeck operators. They show that, under certain conditions, the semigroup is chaotic for the one-dimensional model, otherwise, it is supercyclic but not hypercyclic. For the multi-dimensional case, they obtain similar results.
Conejero, José A., Mangino, Elisabetta M.   +1 more
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Operators Associated with the Ornstein-Uhlenbeck Semigroup

Journal of the London Mathematical Society, 2000
In this paper we apply some of the arguments and techniques developed in [\textit{T. Menárguez}, \textit{S. Pérez} and \textit{F. Soria}, J. Lond. Math. Soc., II. Ser. 61, No. 3, 846-856 (2000; preceding review)] for the study of the boundedness of certain operators associated with the Ornstein-Uhlenbeck semigroup.
Pérez, Sonsoles, Soria, Fernando
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Harnack inequality for Ornstein–Uhlenbeck type operators

Archiv der Mathematik, 2020
The author proves a Harnack inequality for non-negative global weak solutions of the equation \(u_t -Lu = 0\), where \(L\) is the second-order elliptic operator \[L = \operatorname{div}(Q(t, x)\nabla ) + \langle B(x) + F(t, x), \nabla \rangle,\] where \(Q\) is uniformly elliptic, \(F\) is bounded, and \(B\) is twice differentiable with bounded ...
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Ornstein–Uhlenbeck operators and semigroups

Russian Mathematical Surveys, 2018
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MAXIMAL OPERATORS FOR THE HOLOMORPHIC ORNSTEIN–UHLENBECK SEMIGROUP

Journal of the London Mathematical Society, 2003
The authors consider the Ornstein-Uhlenbeck semigroup on a finite dimensional Euclidean space \(R^d\) with Gaussian measure \(d \gamma = \pi^{-d/2} e^{-| x| ^2}\, dx\). It is a symmetric diffusion semigroup \(\{ {\mathcal H}_t: t \geq 0 \}\) whose kernel \(h_t\) has an analytic continuation to a distribution-valued function \(z \to h_z\), which is ...
GARCIA CUERVA J., MAUCERI, GIANCARLO, MEDA S., SJOGREN P., TORREA J. L.   +4 more
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Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2009
Summary: Replacing the Gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on \(\mathbb{R}^d\), we define the notion of Kolmogorov kernel estimates. This allows us to show that, under Dirichlet boundary conditions, Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-)contractive \(C_0\)-semigroups
Wiedl, Julian, Haller-Dintelmann, Robert
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Kolmogorov Equations for Degenerate Ornstein–Uhlenbeck Operators

Siberian Mathematical Journal
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V. I. Bogachev, S. V. Shaposhnikov
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Higher-order Riesz operators for the Ornstein–Uhlenbeck Semigroup

Potential Analysis, 1999
The Riesz operator of order \(\alpha\) on the space weighted with the Gaussian measure \(d\gamma=e^{-|x|^2}dx\) is the operator \(D^\alpha L^{-\frac{|\alpha|}{2}}\Pi_0\), where the operator \(L=-\frac{1}{2}\Delta+x\cdot \nabla\) is the natural Laplacian and \(\Pi_0\) is the extended orthogonal projection from \(L^2(\gamma)\) on the domain of definition
GARCIA CUERVA J., MAUCERI, GIANCARLO, SJOGREN P., TORREA J. L.   +3 more
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Ornstein–Uhlenbeck operators with time periodic coefficients

Journal of Evolution Equations, 2007
We study the realization of the differential operator \(u \mapsto u_t - L(t)u\) in the space of continuous time periodic functions, and in L2 with respect to its (unique) invariant measure. Here L(t) is an Ornstein-Uhlenbeck operator in \({\mathbb{R}}^n\), such that L(t + T) = L(t) for each \(t \in {\mathbb{R}}\).
DA PRATO G, LUNARDI, Alessandra
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