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作者：Cavalier, L; Tsybakov, A
作者单位：Aix-Marseille Universite; Sorbonne Universite; Universite Paris Cite
摘要：We consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems, in particular multivariate ones. We propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale (that includes ellipoids with polynomially and exponentially decreasing axes) and, at the same time, satisfies asymptotically exact oracle inequalities within a...
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作者：Stannat, W
作者单位：University of Bielefeld
摘要：Let A be a Feller generator on a compact space and L be the corresponding Fleming-Viot (FV) operator with no selection and no recombination. In this paper we give conditions on A implying that the semigroup (T-t) generated by L (i) converges towards equilibrium with exponential rate (moreover, we determine explicit bounds on the rate of convergence in terms of A), (ii) is hypercontractive, (iii) is strong Feller, and (iv) is compact, We give applications of the last result to the existence of ...
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作者：Carmona, P; Hu, Y
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：The purpose of this work is the study of the partition function Z(n) (beta) of a (d + 1)-dimensional lattice directed polymer in a Gaussian random environment (beta > 0 being the inverse of temperature). In the low-dimensional cases (d = 1 or d = 2), we prove that for all beta > 0, the renormalized partition function Z(n) (beta)/EZ(n) (beta) converges to 0 and the,))() of two independent configurations does not converge to 0. In the correlation ((n)) high dimensional case (d > 3), a lower tail...
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作者：Collet, P; Martinez, S; Schmitt, B
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universidad de Chile; Universidad de Chile; Universite Bourgogne Europe
摘要：We prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval. As an immediate corollary we obtain a concentration inequality. We apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure.
