Searched for: subject%3A%22UMD%255C+Banach%255C+space%22
(1 - 15 of 15)
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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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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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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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Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
journal article 2008
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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
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Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
conference paper 2007
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Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
journal article 2007
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Cox, S. (author), Veraar, M. (author)
journal article 2007
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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 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
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