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作者：MASON, DM; SHORACK, GR
作者单位：University of Washington; University of Washington Seattle
摘要：It is now classical that the sample mean YBAR is known to be asymptotically normal with square-root n norming if and only if 0 < Var[Y] < infinity and with arbitrary norming if and only if the df of Y is in the domain of attraction of the normal df. Now let T(n) = n-1SIGMAc(ni)h(X(n:i)) for order statistics X(n:i) from a df F denote a general L-statistic subject to a bit of regularity; the key condition introduced into this problem in this paper is the regular variation of the score function J...
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作者：FINNER, H
摘要：The main result of this article is a generalization of the generalized Holder inequality for functions or random variables defined on lower-dimensional subspaces of n-dimensional product spaces. It will be seen that various other inequalities are included in this approach. For example, it allows the calculation of upper bounds for the product measure of n-dimensional sets with the help of product measures of lower-dimensional marginal sets. Furthermore, it yields an interesting inequality for ...
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作者：LAWLER, GF; BRAMSON, M; GRIFFEATH, D
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We study the asymptotic shape of the occupied region for an interacting lattice system proposed recently by Diaconis and Fulton. In this model particles are repeatedly dropped at the origin of the d-dimensional integers. Each successive particle then performs an independent simple random walk until it sticks at the first site not previously occupied. Our main theorem asserts that as the cluster of stuck particles grows, its shape approaches a Euclidean ball. The proof of this result involves G...
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作者：CHEN, LHY; CHOI, KP
摘要：Let X(n1),...,X(nn), n greater-than-or-equal-to 1, be independent random variables with P(X(ni) = 1) = 1 - P(X(ni) = 0) = p(ni) such that max{p(ni): 1 less-than-or-equal-to i less-than-or-equal-to n} --> 0 as n --> infinity. Let W(n) = SIGMA1 less-than-or-equal-to k less-than-or-equal-to n X(nk) and let Z be a Poisson random variable with mean lambda = EW(n). Poisson approximation for the distribution of W(n) dates back to 1960, when Le Cam obtained upper bounds for the total variation distanc...
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作者：BARBOUR, AD; CHEN, LHY; LOH, WL
作者单位：National University of Singapore; Purdue University System; Purdue University
摘要：The aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS(v), where v is a finite positive measure on (0, infinity). A number of results related to these distributions are established. These in turn are used in a number of examples to give bounds for the error in the compound Poisson approximation to the distribution of a sum of random variables.
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作者：MILLET, A; NUALART, D; SANZ, M
作者单位：University of Barcelona
摘要：Consider the family of perturbed stochastic differential equations on R(d), X(t)e = X0e = square-root e integral-0/t sigma(X(s)e) . dW(s) + integral-0/t b(X(s)e) ds, e > 0, defined on the canonical space associated with the standard k-dimensional Wiener process W. We assume that {X0e, e > 0} is a family of random vectors not necessarily adapted and that the stochastic integral is a generalized Stratonovich integral. In this paper we prove large deviations estimates for the laws of {X.e, e > 0}...
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作者：FLEISCHMANN, K; GREVEN, A
作者单位：University of Gottingen
摘要：We consider a continuous time branching random walk on the finite set {1, 2,..., N} with totally symmetric diffusion jumps and some site-dependent i.i.d. random birth rates which are unbounded. We study this process as the time t and the space size N tend to infinity simultaneously. In the classical law of large numbers setup for spatial branching models, the growth of the population obeys an exponential limit law due to the localization of the overwhelming portion of particles in the record p...
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作者：HOUDRE, C
摘要：We obtain criteria for the SLLN to hold for processes which are Fourier transforms of random measures. With this spectral approach, we also give criteria for the pointwise ergodic theorem to hold, for some classes of operators between L(alpha)-spaces, 1 less-than-or-equal-to alpha < + infinity. These results apply in particular to contractions on L2. Some random fields extensions are also studied.
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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...
