Tze Leng Lai, Qi-Man Shao, Qiying Wang (2012)
ESAIM: Probability and Statistics
Similarity:
Let be a Studentized U-statistic. It is proved that a Cramér type moderate deviation ( ≥ )/(1 − Φ()) → 1 holds uniformly in [0, ( )) when the kernel satisfies some regular conditions.
LU Yong (2012)
ESAIM: Proceedings
Similarity:
We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies (1 ) and amplitude (1), over long time intervals (1 ), in the limit → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].
Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)
ESAIM: Probability and Statistics
Similarity:
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function : × → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic...
Alessio Figalli, Nicola Gigli (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We prove that any Kantorovich potential for the cost function = /2 on a Riemannian manifold (, ) is locally semiconvex in the “region of interest”, without any compactness assumption on , nor any assumption on its curvature. Such a region of interest is of full -measure as soon as the starting measure does not charge – 1-dimensional rectifiable sets.