Rate of convergence for the Donsker theorem for rough paths The Donsker theorem says that a random walk, when conveniently rescaled, converges to a Brownian motion. A finer result of Friz and Victoir, that the Lévy area of the random walk goes also to the Lévy area of the Brownian motion. The question is…
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One of many advantages of the Stein’s method is its versatility. It can be applied to prove convergence to Gaussian random variables or processes as well as to Poisson random variables or point processes. In this new paper, we investigate this last aspect showing that some multi-points transformation of some point processes lead to a…
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We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an…
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Algebraic topology has been extensively and successfully used in image processing for a long time. In telecommunication networks, it can be used to verify that a zone in the plane is fully covered by a set of base stations with a few informations on their relative locations. In this article, we compute some of the…
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