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作者：SHEEHY, A; WELLNER, JA
作者单位：University of Washington; University of Washington Seattle
摘要：A class F of measurable functions on a probability space (A, A, P) is called a P-Donsker class and we also write F is-an-element-of CLT(P), if the empirical processes X(n)P = square-root n (P(n) - P) converge weakly to a P-Brownian bridge G(P) having bounded uniformly continuous sample paths almost surely. If this convergence holds for every probability measure P on (A, A), then F is called a universal Donsker class and we write F is-an-element-of CLT(M), where M = {all probability measures on...
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作者：EINMAHL, JHJ
摘要：The tail empirical process is defined to be for each n is-an-element-of N, w(n)(t) = (n/k(n))1/2-alpha(n)(tk(n)/n), 0 less-than-or-equal-to t less-than-or-equal-to 1, where alpha(n) is the empirical process based on the first n of a sequence of independent uniform (0, 1) random variables and {k(n)}n=1infinity is a sequence of positive numbers with k(n)/n --> 0 and k(n) --> infinity. In this paper a complete description of the almost sure behavior of the weighted empirical process alpha(n)alpha...
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作者：PITTEL, B
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作者：ROCKNER, M
摘要：We study the positive parabolic functions of the Ornstein-Uhlenbeck operator on an abstract Wiener space E using the approach developed by Dynkin. This involves first proving a characterization of the entrance space of the corresponding Ornstein-Uhlenbeck semigroup and deriving an integral representation for an arbitrary entrance law in terms of extreme ones. It is shown that the Cameron-Martin densities are extreme parabolic functions, but that if dim E = infinity, not every positive paraboli...
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作者：ZABELL, SL
摘要：A probability measure on the sphere is absolutely continuous with respect to the uniform measure on the sphere if and only if the probability of any open set varies continuously as the sphere is rotated. In general, if a topological group G acts transitively on a topological space S, and both are Hausdorff, locally compact and second countable, then a probability measure v on the Borel sets of S is absolutely continuous with respect to the unique invariant measure class on S if and only if the...
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作者：KESTEN, H; MALLER, RA
作者单位：University of Western Australia
摘要：Let X(i) be independent and identically distributed random variables with distribution F. Let M(n)(n) less-than-or-equal-to ... less-than-or-equal-to M(n)(1) be the sample X1, X2,..., X(n) arranged in increasing order, with a convention for the breaking of ties, and let X(n)(n),..., X(n)(1) be the sample arranged in increasing order of modulus, again with a convention to break ties. Let S(n) = X1 + ... +X(n) be the sample sum. We consider sums trimmed by large values, (r)S(n) = S(n) - M(n)(1) ...
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作者：NOBLE, C
作者单位：University System of Ohio; Oberlin College
摘要：The sexual reproduction process is a reaction-diffusion type interacting particle system which exhibits phase transition. In this paper an upper bound is given for the critical value of the reaction rate and the equilibrium density is determined for all noncritical values of the reaction rate. The method of renormalized bond construction is the basis of our proof. Results for the hydrodynamic limit of the process are employed and some results for the associated nonlinear partial differential e...
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作者：GILAT, D; HILL, TP
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refinement of the Glivenko-Cantelli theorem is obtained, in which a new empirical distribution function not only has the usual uniformly...
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作者：BERMAN, SM
摘要：Let X(t) be a stationary vector Gaussian process in R(m) whose components are independent copies of a real stationary Gaussian process with covariance function r(t). Let phi(z) be the standard normal density and, for t > 0, epsilon > 0, consider the double integral [GRAPHICS] which represents an approximate self-intersection local time of X(s), 0 less-than-or-equal-to s less-than-or-equal-to t. Under the sole condition r is-an-element-of L2, the double integral has, upon suitable normalization...
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作者：WOOD, GR
摘要：We answer two questions: What is the probability that a randomly chosen distribution function on {0, 1,..., n} is a mixture of binomial distributions? and What is the probability that an n-exchangeable sequence is the initial segment of an infinite exchangeable sequence? Curiously, the answers are the same.
