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作者：HALL, P
摘要：Laws of the iterated logarithm are derived for row sums of triangular arrays of independent random variables, in the context of nonparametric regression estimators. These laws provide exact strong convergence rates for kernel type nonparametric regression estimators. They apply to the important case where design points are conditioned upon, and permit the design to be multivariate. We impose minimal conditions on the error distribution; in fact, only finite variance is needed.
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作者：BASS, RF; PEI, H
作者单位：Northwestern University
摘要：Bounds are found on the transition densities and Green functions for Brownian motion with normal reflection in Holder and Lipschitz domains. For Lipschitz domains, reflecting Brownian motion and boundary local time are constructed, a Harnack inequality valid up to the boundary is proved, a probabilistic solution to the Neumann problem is given and the Kuramochi boundary is identified.
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作者：PAPAMARCOU, A; FINE, TL
作者单位：University System of Maryland; University of Maryland College Park; Cornell University
摘要：We discuss issues of existence and stochastic modeling in regard to sequences that exhibit combined features of independence and instability of relative frequencies of marginal events. The concept of independence used here is borrowed from the frequentist account of numerical probability advanced by von Mises: A sequence is independent if certain salient asymptotic properties are invariant under the causal selection of subsequences. We show that independence (in the above sense) and instabilit...
