108 citations · 236 across the 36 of their papers we have counts for
14 papers · 1 filter
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…
Maximal estimates for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations
Jan van Neerven, Mark Veraar
This paper presents a survey of maximal inequalities for stochastic convolutions in -smooth Banach spaces and their applications to stochastic evolution equations.
Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes
Jan van Neerven, Mark Veraar
We prove a new Burkholder-Rosenthal type inequality for discrete-time processes taking values in a 2-smooth Banach space. As a first application we prove that if $(S(t,s))_{0\leq s…
Second quantisation for skew convolution products of infinitely divisible measures
David Applebaum, Jan van Neerven
Suppose and are infinitely divisible Radon measures on real Banach spaces and , respectively and let be a Borel measurable mappin…
Poisson stochastic integration in Banach spaces
Sjoerd Dirksen, Jan Maas, Jan van Neerven
We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non…
Second quantisation for skew convolution products of measures in Banach spaces
David Applebaum, Jan van Neerven
We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that unde…
Stochastic integration in Banach spaces - a survey
Jan van Neerven, Mark Veraar, Lutz Weis
This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are…
Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion
Bohdan Maslowski, Jan van Neerven
We obtain necessary and sufficient conditions for equivalence of law for linear stochastic evolution equations driven by a general Gaussian noise by identifying the suitable space…
A maximal inequality for stochastic convolutions in 2-smooth Banach spaces
Jan van Neerven, Jiahui Zhu
Let (e^{tA})_{t \geq 0} be a C_0-contraction semigroup on a 2-smooth Banach space E, let (W_t)_{t \geq 0} be a cylindrical Brownian motion in a Hilbert space H, and let (g_t)_{t \g…
Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations
Markus Kunze, Jan van Neerven
We prove convergence of the solutions X_n of semilinear stochastic evolution equations dX_n(t) = (A_nX(t) + F_n(t,X_n(t)))dt + G_n(t,X_n(t))dW_H(t), X_n(0) = x_n, on a Banach space…
Maximal -regularity for stochastic evolution equations
Jan van Neerven, Mark Veraar, Lutz Weis
We prove maximal -regularity for the stochastic evolution equation \[\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {a…
Stochastic maximal -regularity
Jan van Neerven, Mark Veraar, Lutz Weis
In this article we prove a maximal -regularity result for stochastic convolutions, which extends Krylov's basic mixed -inequality for the Laplace operator on ${\math…
Approximating the coefficients in semilinear stochastic partial differential equations
Markus Kunze, Jan van Neerven
We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with mul…
Stochastic evolution equations driven by Liouville fractional Brownian motion
Zdzislaw Brzezniak, Jan van Neerven, Donna Salopek
Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian m…