Searched for: subject%3A%22banach%255C+space%22
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Kirchner, K. (author), Schwab, Christoph (author)
We formulate standard and multilevel Monte Carlo methods for the kth moment M<sub>ε</sub><sup>k</sup>[ξ] of a Banach space valued random variable ξ:Ω→E, interpreted as an element of the k-fold injective tensor product space ⊗<sub>ε</sub><sup>k</sup>E. For the standard Monte Carlo estimator of M<sub>ε</sub><sup>k</sup>[ξ], we prove the k...
journal article 2024
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Lindemulder, N. (author)
We study the pointwise multiplier property of the characteristic function of the half-space on weighted mixed-norm anisotropic vector-valued function spaces of Bessel potential and Triebel–Lizorkin type.
journal article 2022
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Kouhkani, S. (author), Koppelaar, H. (author), Taghipour Birgani, O. (author), Argyros, I. K. (author), Radenović, S. (author)
The objective in this article is to extend the applicability of Newton’s method for solving Banach space valued nonlinear equations. In particular, a new semi-local convergence criterion for Newton’s method (NM) based on Kantorovich theorem in Banach space is developed by application of the Heisenberg Uncertainty Principle (HUP). The...
review 2022
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Lorist, E. (author)
In this dissertation we develop vector-valued harmonic analysis methods. Particular emphasis is put on the study of stochastic singular integral operators, which arise naturally in the study of SPDE.
doctoral thesis 2021
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van Neerven, J.M.A.M. (author), Veraar, M.C. (author)
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)) <sub>⩽</sub><sub>s</sub><sub>≤</sub><sub>t</sub><sub>⩽</sub><sub>T</sub> is a C-evolution family of contractions on a 2-smooth Banach space X and (Wt)t∈[0,T] is a...
journal article 2021
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Dominguez, Oscar (author), Veraar, M.C. (author)
In this paper we study the vector-valued analogues of several inequalities for the Fourier transform. In particular, we consider the inequalities of Hausdorff–Young, Hardy–Littlewood, Paley, Pitt, Bochkarev and Zygmund. The Pitt inequalities include the Hausdorff–Young and Hardy–Littlewood inequalities and state that the Fourier transform is...
journal article 2021
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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 2-smooth 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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Yaroslavtsev, I.S. (author)
This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic L<sup>p</sup>- and ø-estimates, a precise construction of a decoupled tangent martin-gale, new estimates for vector-valued stochastic integrals, and several other claims concerning tangent martingales and...
journal article 2020
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Ondrejat, Martin (author), Veraar, M.C. (author)
We show that paths of solutions to parabolic stochastic differential equations have the same regularity in time as the Wiener process (as of the current state of art). The temporal regularity is considered in the Besov-Orlicz space Bϕ <sup>1/</sup><sub>2</sub><sup>2</sup><sub>∞</sub>(0,T;X)where ϕ<sub>2</sub>(x)= exp(x<sup>2</sup>)− 1 and X...
journal article 2020
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Lindemulder, N. (author)
This thesis is concerned with the maximal regularity problem for parabolic boundary value problems with inhomogeneous boundary conditions in the setting of weighted function spaces and related function space theoretic problems.<br/>This in particularly includes weighted $L_{q}$-$L_{p}$-maximal regularity but also weighted $L_{q}$-maximal...
doctoral thesis 2019
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Yaroslavtsev, I.S. (author)
In this thesis we study martingales and stochastic integration of processes with<br/>values in UMD Banach spaces.
doctoral thesis 2019
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Yaroslavtsev, I.S. (author)
In this paper, we consider Meyer–Yoeurp decompositions for UMD Banach space-valued martingales. Namely, we prove that X is a UMD Banach space if and only if for any fixed p ∈ (1, ∞), any X-valued L<sup>p</sup>-martingale M has a unique decomposition M = M<sup>d</sup> + M<sup>c</sup> such that M<sup>d</sup> is a purely discontinuous martingale...
journal article 2019
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Lü, Qi (author), van Neerven, J.M.A.M. (author)
Extending results of Pardoux–Peng and Hu–Peng, we prove well-posedness results for backward stochastic evolution equations in UMD Banach spaces.
book chapter 2019
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Yaroslavtsev, I.S. (author)
We introduce the notion of weak differential subordination for martingales, and show that a Banach space X is UMD if and only if for all p ∈ (1, ∞) and all purely discontinuous X-valued martingales M and N such that N is weakly differentially subordinated to M, one has the estimate E || N<sub>∞</sub> ||<sup>p</sup> ≤ C<sub>p</sub>E|| M<sub>∞<...
journal article 2018
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Yaroslavtsev, I.S. (author)
In this paper we show sharp lower bounds for norms of even homogeneous Fourier multipliers in L(L<sup>p</sup>(R<sup>d</sup>;X)) for 1&lt;p&lt;∞and for a UMD Banach space X in terms of the range of the corresponding symbol. For example, if the range contains a<sub>1</sub>,…,a<sub>N</sub>∈C, then the norm of the multiplier exceeds ‖a<sub>1</sub...
journal article 2018
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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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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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Veraar, M. (author)
journal article 2009
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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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