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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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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<p<∞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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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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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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- 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) journal article 2007
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- Cox, S. (author), Veraar, M. (author) journal article 2007