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作者：Marton, K
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：Let q(n) be a continuous density function in n-dimensional Euclidean space. We think of q(n) as the density function of some random sequence X-n with values in R-n. For I subset of [1. n], let X-I denote the collection of coordinates X-i, i is an element of I, and let X-I, denote the collection of coordinates X-i, i is not an element of I. We denote by Q(I)(x(I)\x(I)) the joint conditional density function of X-I, given X-I. We prove measure concentration for q in the case when, for an appropr...
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作者：Albeverio, S; Ferrario, B
作者单位：University of Bonn; University of Pavia
摘要：A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure mu(v) whose covariance is given in terms of the enstrophy. Pathwise uniqueness for mu(v)-a.e. initial velocity is proven for solutions having mu(v) as invariant measure.
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作者：Richards, DS
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Let (L,less than or equal to) be a finite distributive lattice, and suppose that the functions f(1), f(2): L --> R are monotone increasing with respect to the partial order less than or equal to. Given mu a probability measure on L, denote by E(f(i)) the average of f(i) over L with respect to mu, i = 1, 2. Then the FKG inequality provides a condition on the measure g under which the covariance, Cov(f(1), f(2)) := E(f(1)f(2)) - E(f(1))E(f(2)), is nonnegative. In this paper we derive a third-ord...
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作者：Pipiras, V; Taqqu, MS
作者单位：Boston University
摘要：We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show how to identify them among general stationary stable processes. We conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components: 1. A mixed moving average component. 2. A harmonizable ...
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作者：Bernardin, C
作者单位：Universite Paris Saclay
摘要：We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density rho. We prove that for dimension d = 2 the occupation time of the site 0 is diffusive as soon as rho not equal 1/2. For dimension d = 1, if the density rho is equal to 1/2, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as t(5/4).
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作者：Hug, D; Reitzner, M; Schneider, R
作者单位：University of Freiburg; Technische Universitat Wien
摘要：In the early 1940s, D. G. Kendall conjectured that the shape of the zero cell of the random tessellation generated by a stationary and isotropic Poisson line process in the plane tends to circularity given that the area of the zero cell tends to infinity. A proof was given by I. N. Kovalenko in 1997. This paper generalizes Kovalenko's result in two directions: to higher dimensions and to not necessarily isotropic stationary Poisson hyperplane processes. In the anisotropic case, the asymptotic ...
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作者：Martin, JB
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We consider directed first-passage and last-passage percolation on the nonnegative lattice Z(+)(d), d greater than or equal to 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x) = lim(n-->infinity)n(-1)T([nx]) exist and are constant a.s. for x is an element of R-+(d), where T(z) is the passage time from the origin to the vertex z is an element of Z(+)(d). We show that this shape function g is continuous on R-+(d), ...
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作者：Berti, P; Pratelli, L; Rigo, P
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：A new type of stochastic dependence for a sequence of random variables is introduced and studied. Precisely, (X-n)ngreater than or equal to1 is said to be conditionally identically distributed (c.i.d.), with respect to a filtration (g(n))(ngreater than or equal to0), if it is adapted to (g(n))(ngreater than or equal to0) and, for each ngreater than or equal to0, (X-k)(k>n) is identically distributed given the past g(n). In case g(0) = {theta, Omega} and g(n) = sigma(X-1,...,X-n), a result of K...
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作者：Wu, WB; Woodroofe, M
作者单位：University of Chicago; University of Michigan System; University of Michigan
摘要：Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating martingales satisfy a Lindeberg-Feller condition. Using the explicit construction of the approximating marti...
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作者：Mason, DM
作者单位：University of Delaware
摘要：We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.
