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作者：MUELLER, C
摘要：We consider the heat equation with a noise term, on a finite interval with periodic boundary conditions. We show how to construct coupled solutions to the equation. As applications, we prove the uniqueness of invariant measures and the triviality of bounded harmonic functions.
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作者：BERKES, I; DEHLING, H
作者单位：University of Groningen
摘要：Motivated by recent results on pathwise central limit theorems, we study in a systematic way log-average versions of classical limit theorems. For partial sums S(k) of independent r.v.'s we prove under mild technical conditions that (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)I{S(k)/a(k) is-an-element-of .} --> G(.) (a.s.) if and only if (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)P(S(k)/a(k) is-an-element-of .) --> G(.). A functional version of this result also holds. For partial sums of ...
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作者：DYNKIN, EB
摘要：The subject of this article is a class of measure-valued Markov processes. A typical example is super-Brownian motion . The Laplacian DELTA plays a fundamental role in the theory of Brownian motion. For super-Brownian motion, an analogous role is played by the operator DELTAu - psi(u), where a nonlinear function psi describes the branching mechanism. The class of admissible functions psi includes the family psi(u) = u(alpha), 1 < alpha less-than-or-equal-to 2. Super-Brownian motion belongs to ...
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作者：LEE, TY
摘要：The empirical measure, a generalization of occupation times, of a super-Brownian motion is studied. In our case the empirical measure tends almost surely to Lebesgue measure as time t --> infinity. Asymptotic probabilities of deviation from this central behavior by various orders (large, not very large and normal deviations) are estimated. Extension to similar superprocesses, that is, Dawson-Watanabe processes, is discussed. Our analytic approach also produces new results for semilinear PDE's.
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作者：CUTLAND, N; NG, SA
摘要：The Loeb measure construction of nonstandard analysis is used to define uniform probability mu(L) on the infinite-dimensional sphere of Poincare, Wiener and Levy, and we construct Wiener measure from it, thus giving rigorous sense to the informal discussion by McKean. From this follows an elementary proof of a weak convergence result. The relation to the infinite product of Gaussian measures is studied. We investigate transformations of the sphere induced by shifts and the associated transform...
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作者：HE, YJ
摘要：A class of topological semigroups called GZH-semigroups is introduced. Conditions under which they have the property that limits of infinitesimal arrays are infinitely divisible are obtained. The convolution semigroup of all probability measures on a second countable LCA-group or on a real separable Hilbert space as well as the semigroup of all positive definite kernels defined on a countable set with complex values and with norms not greater than 1 are reduced to an extended form of Delphic s...
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作者：SATO, KI
摘要：For any positive integer n, there exists a unimodal distribution mu such that mu * mu is n-modal. Furthermore, there is a unimodal distribution mu such that mu * mu has infinitely many modes. Lattice analogues of the results are also given.
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作者：SKALA, HJ
摘要：In an important paper, Strassen discussed the existence of measures on product spaces with given marginals in the context of Polish spaces. We generalize his results to arbitrary Hausdorff spaces and indicate some applications such as measures with given support and stochastic inequalities on partially ordered Hausdorff spaces, In the second part of our paper, we state two results on the general moment problem, thus generalizing earlier theorems due to Kemperman.
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作者：ONEIL, KA; REDNER, RA
摘要：The limiting distribution of weighted U-statistics of degree 2 is found for a wide class of weights, including uniform weights. Nonnormal limits can occur for both degenerate and nondegenerate kernels. A compact expression is given for the cumulants of the distribution. Incomplete and randomly weighted U-statistics are also analyzed.
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作者：BOIVIN, D
作者单位：University System of Ohio; Ohio State University
摘要：Assign to each edge e of the square lattice Z2 a random bond conductivity c(e). If c(e) are stationary, ergodic and such that 0 < a < c(e) < b < infinity for all edges e, then there is a central limit theorem for the corresponding reversible random walk on the lattice which holds for almost all environments.
