Compactness in vector-valued banach function spaces

Electrical Engineering, Mathematics and Computer Scienc

A Clark-Occone formula in UMD Banach spaces

Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Invariant measures for stochastic cauchy problems with asymptotically unstable drift semigroup

We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the formDelft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise

Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

A semigroup approach to stochastic delay equations in spaces of continuous functions

Electrical Engineering, Mathematics and Computer Scienc

On the domain of nonsymmetric Ornstein-Uhlenbeck operators in Banach spaces

Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

On the action of Lipschitz functions on vector-valued random sums

Electrical Engineering, Mathematics and Computer Scienc

On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions

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.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Conical square function estimates in UMD Banach spaces and applications to H?-functional calculi

We study conical square function estimates for Banach-valued functions and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-M(c)Intosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator A with certain off-diagonal bounds such that A always has a bounded H-infinity-functional calculus on these spaces. This provides a new way of proving functional calculus of A on the Bochner spaces L-p(R-n; X) by checking appropriate conical square function estimates and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when X = C, our approach gives refined p-dependent versions of known resultsDelft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Space-time regularity of solutions of the parabolic stochastic Cauchy problem

Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc