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作者：Bobkov, Sergey G.; Ledoux, Michel
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Brascamp-Lieb-type, weighted Poincare-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general kappa-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinite-dimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of this family of measures. Cheeger-type isoperimetric inequalities are investigated similarly, gi...
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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13; Universite Paris Cite; Sorbonne Universite
摘要：We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers a question of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609-631]. Our method applies, furthermore, to the study of directed polymers on a disordered tree. In particular, we give a rigorous proof of a phase transition phenomenon for the partition function (from the point of view of conv...
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作者：Unterberger, Jeremie
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
摘要：The d-dimensional fractional Brownian motion (FBM for short) B(t) = ((B(t)((1)),...,B(t)((d))), t is an element of R) with Hurst exponent alpha, alpha is an element of (0, 1), is a d-dimensional centered, self-similar Gaussian process with covariance E[B(s)((i)) B(t)((j))] = 1/2 delta(i), j (vertical bar s vertical bar(2 alpha) + vertical bar t vertical bar(2 alpha) - vertical bar t -s vertical bar(2 alpha)). The long-standing problem of defining a stochastic integration with respect to FBM (a...
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作者：Zhang, Xicheng
作者单位：University of New South Wales Sydney; Huazhong University of Science & Technology
摘要：In this paper we first prove a Clark-Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational representation formula for the Laplace transform of bounded Poisson functionals, which has been conjectured by Dupuis and Ellis [A Weak Convergence Approach to the Theory of Large Deviations (1997) Wiley], p. 122.
