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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)
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