6 papers
The bounds and are sharp
Emiel Lorist, Jan van Neerven
It was proved in the 1980s by Burkholder and Bourgain that, for any Banach space and , the UMD property for is equivalent to boundedness of the Hilbert tran…
Dimension-free -calculus of angle for UMD-valued Ornstein--Uhlenbeck operators
Jan van Neerven
Let , let be a UMD Banach space, let , and let be the generator of the Ornstein--Uhlenbeck semigroup on $L^p(\mathbb R^d,γ_d;…
Necessary conditions for deterministic and stochastic maximal regularity
Emiel Lorist, Jan van Neerven, Mark Veraar +1
We study the role of Banach space geometry in deterministic and stochastic maximal regularity. We first construct an example showing that the UMD assumption in the characterisation…
A Bismut-Elworthy-Li formula for linear stochastic evolution equations in Banach spaces
Jan van Neerven
We prove a Bismut-Elworthy-Li formula for linear stochastic evolution equations in Banach spaces. The admissible directions are those for which the deterministic orbit is square in…
Holevo classicalisation and context integration: Global versus protocolwise integration
Jan van Neerven, Marijn Waaijer
Suppose that a family of commutative measurement contexts is given, together with the corresponding classical probability laws. We study the problem under what conditions these con…
Lévy measures on Banach spaces
Jan van Neerven, Markus Riedle
We establish an explicit characterisation of Lévy measures on both -spaces and UMD Banach spaces. In the case of -spaces, Lévy measures are characterised by an integrabil…