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作者：Bobkov, S
摘要：The isoperimetric problem for log-concave product measures in R(n) equipped with the uniform distance is considered. Necessary and sufficient conditions under which standard half-spaces are extremal are presented.
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作者：Bercovici, H; Pata, V
摘要：Let X(1),X(2),... be a sequence of free identically distributed random variables, with common distribution mu. It was shown by Lindsay and Pata, in a more general context, that a sufficient condition for the weak law of large numbers to hold for the sequence X(1), X(2),... is that (t-->infinity)lim t mu({x: \x\ > t}) = 0. We show that this condition is necessary as well as sufficient. Even though the condition is identical with the corresponding one for commuting independent variables, the pro...
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作者：Newman, CM; Volchan, SB
摘要：Consider an inhomogeneous contact process on Z(1) in which the recovery rates delta(x) at site I: are i.i.d. random variables (bounded above) while the infection rate is a constant epsilon. The condition uP(-log delta(x) > u) --> + infinity as u --> + infinity. implies the survival of the process for every epsilon > 0.
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作者：Pinsky, RG
摘要：We consider the supercritical finite measure-valued diffusion, X(t), whose log-laplace equation is associated with the semilinear equation u(t) = Lu + beta u - alpha u(2), where alpha, beta > 0, and L = 1/2 Sigma(i,j=1)(d) alpha(ij) (partial derivative(2)/(partial derivative x(i) partial derivative x(j))) + Sigma(i=1)(d) b(i) (partial derivative/partial derivative x(i)). A path X(.) is said to survive if X(t) not equal 0, for all t greater than or equal to 0. Since beta > 0, P-mu(X(.) survives...
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作者：Bentkus, V; Gotze, F
摘要：We prove the Berry-Esseen bound for the Student t-statistic. Under the assumption of a third moment this bound coincides (up to an absolute constant) with the classical Berry-Esseen bound for the mean. In general the distribution of the Student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean, and sometimes faster. For example, rates of convergence can be proved if the underlying distribution is in the domain of attraction of the...
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作者：Rosinski, J; Samorodnitsky, G
作者单位：Cornell University
摘要：We consider stochastic processes X = {X(t), t is an element of T} represented as a Levy chaos of finite order, that is, as a finite sum of multiple stochastic integrals with respect to a symmetric infinitely divisible random measure. For a measurable subspace V of RT We prove a very general zero-one law P(X is an element of V) = 0 or 1, providing a complete analog to the corresponding situation in the case of symmetric infinitely divisible processes (single integrals with respect to an infinit...
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作者：Bentkus, V; Gotze, F
摘要：We prove optimal convergence rates in the central limit theorem for sums in R(k). Assuming a fourth moment, we obtain a Berry-Esseen type bound of O(N-1) for the probability of hitting a ball provided that k greater than or equal to 5. The proof still requires a technical assumption related to the independence of coordinates of sums.
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作者：Einmahl, JHJ
摘要：A short proof of the lower bound in the strong version of the famous Theorem IA in Kiefer (1970) on the Bahadur-Kiefer process is presented. The proof is elementary and, in particular, does not use strong approximations.
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作者：Burdzy, K; Werner, W
作者单位：University of Cambridge; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time interval contains almost surely no triple point of this Brownian path.
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作者：DeBlassie, RD
摘要：Existence and uniqueness in law of reflecting Brownian motion in a wedge is proved. The direction of reflection along the sides of the wedge varies in a reasonable fashion, except perhaps at the corner.
