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作者：Penrose, Mathew D.
作者单位：Durham University
摘要：For n points placed uniformly at random on the unit square, suppose M-n (respectively, M-n(1)) denotes the longest edge-length of the nearest neighbor graph (respectively, the minimal spanning tree) on these points. It is known that the distribution of n pi M-n(2) - log n converges weakly to the double exponential; we give a new proof of this. We show that P[M-n(1) = M-n] -> 1, so that the same weak convergence holds for M-n(1).
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作者：Comets, Francis
作者单位：University of California System; University of California Irvine
摘要：We propose a new empirical procedure for detecting phase transition from a single sample of a Gibbs-Markov random field. The method is based on frequencies for large deviations when the whole sample is divided in smaller blocks and estimates for the rate function. We relate our approach to an almost sure large deviation principle.
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作者：Niu, Xu-Feng
作者单位：State University System of Florida; Florida State University; State University System of Florida; Florida State University
摘要：Consider a class of nonstationary time series with the form Y-t = mu t + xi(t) where {xi(t)} is a sequence of infinite moving averages of independent random variables with regularly varying tail probabilities and different scale parameters. In this article, the extreme value theory of {Y-t} is studied. Under mild conditions, convergence results for a point process based on the moving averages are proved, and extremal properties of the nonstationary time series, including the convergence of max...
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作者：Denardo, Eric V.; Feinberg, Eugene A.; Kella, Offer
作者单位：Yale University; State University of New York (SUNY) System; Stony Brook University; Hebrew University of Jerusalem
摘要：This paper deals with first passage heights of sums of renewal sequences, random walks, and Levy processes. We prove that the joint age and excess (and therefore, the current life. stationary distributions of these heights are stochastically increasing (in the usual first-order sense. in the passage levels. As a preliminary tool, which is also of independent interest, a new decomposition of the stationary excess distribution, as a convolution of two other distributions, is developed. As a cons...
