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Agresti, A. (author), Veraar, M.C. (author)In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi or semilinear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz...journal article 2024
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Böhm, Udo (author)The stochastic FitzHughNagumo equations are a system of stochastic partial differential equations that describes the propagation of action potentials along nerve axons. In the present work we obtain wellposedness and regularisation results for the FitzHughNagumo equations with domain R^d. We begin by considering the weak critical variational...master thesis 2023
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Agresti, Antonio (author), Veraar, M.C. (author)This paper is a continuation of Part I of this project, where we developed a new local wellposedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blowup criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical...journal article 2022
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Agresti, Antonio (author), Veraar, M.C. (author)In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi or semilinear type. This first part is on local...journal article 2022
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van Neerven, J.M.A.M. (author), Veraar, M.C. (author)This paper presents a survey of maximal inequalities for stochastic convolutions in 2smooth Banach spaces and their applications to stochastic evolution equations. This article is part of the theme issue 'Semigroup applications everywhere'.review 2020
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Lü, Qi (author), van Neerven, J.M.A.M. (author)Extending results of Pardoux–Peng and Hu–Peng, we prove wellposedness results for backward stochastic evolution equations in UMD Banach spaces.book chapter 2019
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Bruell, G. (author), Ehrnström, Mats (author), Geyer, A. (author), Pei, Long (author)We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms of three principles, based on the structure of the equations. The first principle covers equations that...journal article 2017
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Veraar, M.C. (author), Yaroslavtsev, I.S. (author)In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local martingales we develop a stochastic integration...journal article 2016
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Gallarati, C. (author), Veraar, M.C. (author)In this paper we study maximal Lpregularity for evolution equations with timedependent operators A. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the Lpboundedness of a class of vectorvalued singular integrals which does not rely on Hörmander conditions in the time...journal article 2016
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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
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Pronk, M. (author)In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance mathematical finance and filtration theory. Second,...doctoral thesis 2013
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 Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author) journal article 2012
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 Cox, S.G. (author), Van Neerven, J.M.A.M. (author) journal article 2010
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 Van Neerven, J.M.A.M. (author), Weis, L. (author) journal article 2008
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 Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author) journal article 2008
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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
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Veraar, M.C. (author)Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinitedimensional 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
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Van Gaans, O. (author), Van Neerven, J. (author)We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the formjournal article 2006
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 Van Neerven, J.M.A.M. (author), Weis, L. (author) journal article 2006