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In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation 𝔼 has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use these uncertainty...
The reliable and effective assimilation of measurements and numerical simulations in engineering applications involving computational fluid dynamics is an emerging problem as soon as new devices provide more data. In this paper we are mainly driven by hemodynamics applications, a field where the progressive increment of measures and numerical tools makes this problem particularly up-to-date. We adopt a Bayesian approach to the inclusion of noisy data in the incompressible steady Navier-Stokes equations...
On présente une formule explicite pour la constante de Sobolev logarithmique correspondant à des diffusions réelles ou à des processus entiers de vie et de mort, sous l’hypothèse que certaines quantités, naturellement associées à des inégalités de Hardy dans ce contexte, approchent leur supremum au bord de leur domaine de définition. La preuve se ramène au cas de la constante de Poincaré, à l’aide de comparaisons exactes entre entropie et variances appropriées.
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