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作者：Shao, QM; Yu, H
作者单位：Western University (University of Western Ontario)
摘要：In this paper we establish weak convergence theorems for weighted empirical processes of strong mixing, rho-mixing and associated sequences. We apply these results to obtain Freak convergence of integral functionals of empirical processes and of mean residual life processes in reliability theory. To carry out the proofs, we develop two Rosenthal-type inequalities for strong mixing and associated sequences.
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作者：Liggett, TM
摘要：The contact process on Z(d) is known to have only two fundamental types of behavior: survival and extinction. Recently Pemantle discovered that the phase structure for the contact process on a tree can be more complex. There are three possible types of behavior: strong survival, weak. survival and extinction. He proved that all three occur on homogeneous trees in which each vertex has d + 1 neighbors, provided that d greater than or equal to 3, but he left, open the case d = 2. Since d = 1 cor...
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作者：Yu, H
摘要：By combining the Berbes-Philipp blocking technique and the Csorgo-Revesz quantile transform methods, we find that partial sums of an associated sequence can be approximated almost surely by partial sums of another sequence with Gaussian marginals. A crucial fact is that this latter sequence is still associated with covariances roughly bounded by the covariances of the original sequence, and that one can approximate it by an lid Gaussian process using the Berkes-Philipp method. We require that ...
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作者：vanderVaart, A
摘要：Several classes of functions are shown to be Donsker by an argument based on partitioning the sample space. One example is the class of all nondecreasing functions f: R --> R such that 0 less than or equal to f less than or equal to F for a given function F with integral F-2 dP/root 1 - P < infinity.
