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The multiresolution analysis (MRA) strategy for homogenization consists of two algorithms ; a procedure for extracting the eeective equation for the average or for the coarse scale behavior of the solution to a diierential equation (the reduction process) and a method for building a simpler equation whose solution has the same coarse behavior as the(More)
In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (D p , W p), the space of persistence diagrams equipped with the p-th Wasserstein metric. In(More)
In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular,(More)
This paper uses high-frequency S&P 500 index futures data and data on the VIX index to provide an arbitrage-free explanation of the variance risk premium and its dynamics. Using the high-frequency data only, I select a semiparametric two-factor stochastic volatility model, containing jumps in the price and the stochastic variance. For this model I derive(More)
(Applied mathematics) Abstract This work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by k dimensional planes but which are embedded in a D k dimensional Euclidean space are considered. Assuming one has samples from such a set, possibly(More)
This paper is based on a formulation of the Navier-Stokes equations developed in arxiv:math.PR/0511067 (to appear in Commun. Pure Appl. Math), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take N copies of the above process (each based on independent Wiener processes),(More)
Interacting particle systems have been applied to model the spread of infectious diseases and opinions, interactions between competing species, and evolution of forest landscapes. In this thesis, we study three spatial models arising from from ecology and social sciences. First, in a model introduced by Schelling in 1971, in which families move if they have(More)