document

Maximal ? -regularity

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

In this paper, we prove maximal regularity estimates in “square function spaces” which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results for both deterministic and stochastic equations in L p -spaces with 1<p<?. For stochastic equations, the...

journal article 2015

document

Maximal Lp-Regularity for Stochastic Evolution Equations

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

journal article 2012

document

A note on maximal estimates for stochastic convolutions

Veraar, M. (author), Weis, L. (author)

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.

journal article 2011

document

Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

Veraar, M.C. (author)

journal article 2009

document

R-boundedness of smooth operator-valued functions

Veraar, M. (author), Hytonen, T. (author)

In this paper we study $R$-boundedness of operator families $\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach spaces. Under cotype and type assumptions on $X$ and $Y$ we give sufficient conditions for $R$-boundedness. In the first part we show that certain integral operator are $R$-bounded. This will be used to obtain $R$-boundedness...

journal article 2009

document

Correlation inequalities and applications to vector-valued Gaussian random variables and fractional Brownian motion

Veraar, M. (author)

journal article 2009

document

On Besov regularity of Brownian motions in infinite dimensions

Veraar, M. (author), Hytonen, T. (author)

journal article 2008

document

Stochastic evolution equations in UMD Banach spaces

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

journal article 2008

document

Non-autonomous stochastic Cauchy problems in Banach spaces

Veraar, M.C. (author), Zimmerschied, J. (author)

journal article 2008

document

A note on optimal probability lower bounds for centered random variables

Veraar, M.C. (author)

journal article 2008

document

Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation

Brzezniak, Z. (author), Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and...

journal article 2008

document

Continuous local martingales and stochastic integration in UMD Banach spaces

Veraar, M.C. (author)

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We...

journal article 2007

document

Conditions for stochastic integrability in UMD Banach spaces

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

conference paper 2007

document

Stochastic integration in UMD Banach spaces

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

journal article 2007

document

Some remarks on tangent martingale difference sequences in L1-spaces

Cox, S. (author), Veraar, M. (author)

journal article 2007

document

Stochastic integration in Banach spaces and applications to parabolic evolution equations

Veraar, M.C. (author)

Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness results and regularity properties. To model the...

doctoral thesis 2006

document

Embedding vector-valued Besov spaces into spaces of gamma-radonifying operators

Veraar, M. (author), Kalton, N. (author), Van Neerven, J. (author), Weis, L. (author)

journal article 2006

document

Randomized UMD Banach spaces and decoupling

Veraar, M.C. (author)

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

journal article 2006

document

A stochastic Datko-Pazy theorem

Haak, B.H. (author), Van Neerven, J.M.A.M. (author), Veraar, M.C. (author)

journal article 2006

document

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

Veraar, M. (author), Van Neerven, J. (author)

journal article 2005