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作者：Kleptsina, M. L.; Liptser, R. Sh; Serebrovski, A. P.
作者单位：Russian University of Transport; Tel Aviv University
摘要：We give an approximation for optimal filtering estimates of a diffusion type signal and its observation under contamination affecting their drifts. The method of analysis is based on the averaging principle and convergence in total variation for distributions of signal and observation.
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作者：Lee, Sungchul
作者单位：National University of Singapore
摘要：Let {X-i : i >= 1} be i.i.d. with uniform distribution [-1/2, 1/2](d), d >= 2, and let T-n be a minimal spanning tree on {X-1,..., X-n}. For each strictly positive integer alpha, let N({X-1,..., X-n}; alpha) be the number of vertices of degree alpha in T-n. Then, for each alpha such that P(N({X-1,..., X alpha+1}; alpha) = 1. > 0, we prove a central limit theorem for N({X-1,..., X-n}; alpha).
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作者：Heath, David; Resnick, Sidney; Samorodnitsky, Gennady
作者单位：Cornell University
摘要：We study the time it takes until a fluid queue with a finite, but large, holding capacity reaches the overflow point. The queue is fed by an on/off process with a heavy tailed on distribution which is known to have long memory. It turns out that the expected time until overflow, as a function of capacity L, increases only polynomially fast; so overflows happen much more often than in the classical light tailed case, where the expected overflow time increases as an exponential function of L. Mo...
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作者：Mathew, Thomas; Nordstrom, Kenneth
作者单位：University System of Maryland; University of Maryland Baltimore County; University of Helsinki
摘要：Let X-i and Y-i follow noncentral chi-square distributions with the same degrees of freedom nu(i) and noncentrality parameters delta(2)(i) and delta(2)(i), respectively, for i = 1, ..., n, and let the Xi's be independent and the Yi's independent. A necessary and sufficient condition is obtained under which Sigma(n)(i=1) lambda(i) X-i is stochastically smaller than Sigma(n)(i=1) lambda(i) Y-i for all nonnegative real numbers lambda(1) >= ... >= lambda(n). Reformulating this as a result in geome...
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作者：Rinott, Yosef; Rotar, Vladimir
作者单位：University of California System; University of California San Diego; Russian Academy of Sciences; Central Economics & Mathematics Institute RAS
摘要：This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic set-up provided by a Markov structure that suggests natural coupling variables. More specifically, given a stationary Markov chain X-(t) and a function U=U(X-(t)), we propose a way to study the proximity of U to a normal random variable when the state space is large. We apply the general method...
