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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...
