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作者：DUDLEY, RM
摘要：Differentiability of functionals of the empirical distribution function is extended. The supremum norm is replaced by p-variation seminorms, which are the pth roots of suprema of sums of pth powers of absolute increments of a function over nonoverlapping intervals. Frechet derivatives often exist for such norms when they do not for the supremum norm. For 1 < q < 2, classes of functions uniformly bounded in q-variation are universal and uniform Donsker classes: The central limit theorem for emp...
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作者：GRUBEL, R; PITTS, SM
作者单位：University of London; University College London
摘要：The GI/G/1 queueing model is regarded as a functional which maps the service and interarrival time distributions onto output quantities of interest, such as the stationary waiting time distribution. For the case where the input distributions have densities, techniques from infinite-dimensional analysis are used to obtain derivatives and Taylor series expansions for the functionals. These yield approximations to the output distributions which can be viewed as nonparametric alternatives to param...
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作者：FITZSIMMONS, PJ; GETOOR, RK
摘要：We derive simple explicit formulas for the Fourier-Laplace transforms of the Hilbert transform and related functionals of the local time of a symmetric Levy process. These formulas generalize results of Biane and Yor for Brownian motion. The method of proof provides an explanation (of sorts) for the presence of the hyperbolic functions in such formulas.
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作者：SHIELDS, PC
作者单位：Eotvos Lorand University
摘要：Of interest in DNA analysis is the length L(x1n) of the longest sequence that appears twice in a sequence x1n of length n. Karlin and Ghandour and Arratia and Waterman have shown that if the sequence is a sample path from an i.i.d. or Markov process, then L(x1n) = O(log n). In this paper, examples of ergodic processes are constructed for which the asymptotic growth rate is infinitely often as large as lambda(n), where lambda(n) is subject only to the condition that it be o(n).
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作者：CSAKI, E; CSORGO, M
作者单位：Carleton University
摘要：Let {GAMMA(t), t is-an-element-of R} be a Banach space B-valued stochastic process. Let P be the probability measure generated by GAMMA(.). Assume that GAMMA(.) is P-almost surely continuous with respect to the norm parallel-to parallel-to of B and that there exists a positive nondecreasing function sigma(a), a > 0, such that P{parallel-to GAMMA(t + a) - GAMMA(t)parallel-to greater-than-or-equal-to x-sigma(a)} less-than-or-equal-to K exp(-gamma-x(beta) with some K, gamma, beta > 0. Then, assum...
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作者：FISHER, E
摘要：The Kolmogorov law of the iterated logarithm fails when the boundedness condition on the increments is relaxed. In this paper, we consider this in the martingale setting and establish a lower bound, extending a result known in the independent case.
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作者：KESTEN, H; LAWLER, GF
作者单位：Duke University
摘要：Let X1, X2, ... be independent random variables such that X(j) has distribution F(sigma(j)), where sigma(j) = 1 or 2, and the distributions F(i) have mean 0. Assume that F(i) has a finite q(i)th moment for some 1 < q(i) < 2. Let S(n) = SIGMA-j=1(n)X(j). We show that if q1 + q2 > 3, then lim sup P{S(n) > 0} > 0 and lim sup P{S(n) < 0} > 0 for each sequence {sigma(j)} of ones and twos.
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作者：NUALART, D
摘要：We prove that in continuous time, the extremal elements of the set of adapted random measures on R+2 are Dirac measures, assuming the underlying filtration satisfies the conditional qualitative independence property. This result is deduced from a theorem in discrete time which provides a correspondence between adapted random measures on N2 and two-parameter randomized stopping points in the sense of Baxter and Chacon. As an application we show the existence of optimal stopping points for upper...
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作者：PEDDADA, SD; RICHARDS, DSP
摘要：Let m (greater-than-or-equal-to 2) be a positive integer; I(m) be the m x m identity matrix; and SIGMA and A be symmetric m x m matrices, where SIGMA is positive definite. By proving that the function phi-alpha-(A) = \I(m) - 2iA-SIGMA\-alpha is a characteristic function only if alpha element-of {0, 1/2, 1, 3/2, ..., (m - 2)/2} union [(m - 1)/2, infinity), we establish a conjecture of Eaton. A similar result is established for the rank 1 noncentral Wishart distribution and is conjectured to als...
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作者：MATTHEWS, P
摘要：Given a partial order of N items, a linear extension that is almost uniformly distributed, in the sense of variation distance, is generated. The algorithm runs in polynomial time. The technique used is a coupling for a random walk on a polygonal subset of the unit sphere in R(N). Included is a discussion of how accurately the steps of the random walk must be computed.
