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作者：Chelkak, Dmitry
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any simply connected discrete domain Omega with four marked boundary vertices and are uniform with respect to Omega's which can be very rough, having many fiords and bottlenecks of various widths. Moreover, due to results from [Boundaries of planar graphs, via circle...
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作者：Gonzales-Gargate, Ivan I.; Ruffino, Paulo R.
作者单位：Universidade Estadual de Campinas
摘要：Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order epsilon. An average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to invariant measures on the leaves, as a goes to zero. An estimate of the rate of convergence is given. These results...
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作者：Hillion, Erwan; Johnson, Oliver
作者单位：University of Luxembourg; Aix-Marseille Universite; University of Bristol
摘要：We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou-Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp-Olkin entropy concavity conjecture.
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作者：Beiglboeck, Mathias; Juillet, Nicolas
作者单位：University of Vienna; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：The basic problem of optimal transportation consists in minimizing the expected costs E[c(X-1, X-2)] by varying the joint distribution (X-1, X-2) where the marginal distributions of the random variables X-1 and X-2 are fixed. Inspired by recent applications in mathematical finance and connections with the peacock problem, we study this problem under the additional condition that (X-i)(i=1,2) is a martingale, that is, E[X-2 vertical bar X-1] = X-1. We establish a variational principle for this ...
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作者：Lee, James R.; Peres, Yuval; Smart, Charles K.
作者单位：University of Washington; University of Washington Seattle; Microsoft; University of Chicago
摘要：Consider a discrete-time martingale {X-t} taking values in a Hilbert space H. We show that if for some L >= 1, the bounds E[parallel to Xt+1 - X-t parallel to(2)(H)parallel to X-t] = 1 and parallel to Xt+1 - Xt+1 parallel to(H) <= L are satisfied for all times t >= 0, then there is a constant c = c(L) such that for 1 <= R <= root t, P(parallel to X-t-X0 parallel to(H) <= R) <= cR/root t . Following Lee and Peres [Ann. Probab. 41(2013) 3392-3419], this estimate has applications to small-ball es...
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作者：Xie, Longjie; Zhang, Xicheng
作者单位：Wuhan University
摘要：By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.
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作者：Pekoz, Erol A.; Rollin, Adrian; Ross, Nathan
作者单位：Boston University; National University of Singapore; University of Melbourne
摘要：We study a new class of time inhomogeneous Polya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein's method combined with characterizing the generalized gamma limiting distributions as fixed points of distributional transformations re...
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作者：Balan, Raluca M.; Conus, Daniel
作者单位：University of Ottawa; Lehigh University
摘要：In this article, we consider the stochastic wave and heat equations driven by a Gaussian noise which is spatially homogeneous and behaves in time like a fractional Brownian motion with Hurst index H > 1/2. The solutions of these equations are interpreted in the Skorohod sense. Using Malliavin calculus techniques, we obtain an upper bound for the moments of order p >= 2 of the solution. In the case of the wave equation, we derive a Feynman-Kactype formula for the second moment of the solution, ...
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作者：Czichowsky, Christoph; Schachermayer, Walter
作者单位：University of London; London School Economics & Political Science; University of Vienna
摘要：Given a sequence (M-n)(n=1)(infinity) of nonnegative martingales starting at M-0(n) = 1, we find a sequence of convex combinations (M-n)(n=1)(infinity) and a limiting process X such that (M-n)(n=1)(infinity) converges in probability to X-tau, for all finite stopping times tau. The limiting process X then is an optional strong supermartingale. A counterexample reveals that the convergence in probability cannot be replaced by almost sure convergence in this statement. We also give similar conver...
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作者：Nourdin, Ivan; Nualart, David; Peccati, Giovanni
作者单位：Universite de Lorraine; University of Luxembourg; University of Kansas
摘要：We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39-64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460-3505], and provide a substantial contribution to a recent line of research, focussing on limit theorems on the Wie...
