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作者：ACCARDI, L; LU, YG
摘要：A continuous version of De Finetti's theorem is proved in which the role of the homogeneous product states is played by the independent increment stationary processes on the real line. The proof is based on a conditional, finite De Finetti's theorem (i.e., a result involving only a finite number of random variables and exchangeable conditional expectations rather than exchangeable probabilities). Our technique of proof improves and simplifies a result of Freedman and includes a generalization ...
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作者：CARLSON, JM; GRANNAN, ER; SWINDLE, GH; TOUR, J
作者单位：University of California System; University of California Santa Barbara; AT&T; Nokia Corporation; Nokia Bell Labs; University of California System; University of California Los Angeles
摘要：We establish hydrodynamic limits for a class of attractive, reversible particle systems with an infinite range of interaction. The limiting nonlinear diffusion equations have diffusion coefficients which are functions of the local density, and which have a singularity at a critical value of the density. On open driven systems, these singular diffusion limits explain the observed nontrivial scaling behavior known as self-organized criticality.
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作者：INGLOT, T; LEDWINA, T
摘要：Let alpha(n) be the classical empirical process. Assume T, defined on D[0, 1], satisfies the Lipschitz condition with respect to a weighted sup-norm in D[0, 1]. Explicit bounds for P(T(alpha(n)) greater-than-or-equal-to x(n) square-root n) are obtained for every n greater-than-or-equal-to n0 and all x(n) is-an-element-of (0, sigma], where n0 and sigma are also explicitly given. These bounds lead to moderately large deviations and expansions of the asymptotic large deviations for T(alpha(n)). T...
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作者：ARCONES, MA; GINE, E
作者单位：University of Connecticut
摘要：Necessary and sufficient conditions for the law of large numbers and sufficient conditions for the central limit theorem for U-processes are given. These conditions are in terms of random metric entroPies. The CLT and LLN for VC subgraph classes of functions as well as for classes satisfying bracketing conditions follow as consequences of the general results. In particular, Liu's simplicial depth Process satisfies both the LLN and the CLT. Among the techniques used, randomization, decoupling i...
