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作者：HUGHES, HR
摘要：Let X(t) be Brownian motion on a Riemannian manifold M started at m and let T be the first time X(t) exits a normal ball about m. The first exit time T for M = S3 X H-3 has the same distribution as the first exit time for M = R6. For M = S3 X H-3, T and X(T) are independent random variables.
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作者：LI, DL; RAO, MB; WANG, XC
作者单位：Jilin University; North Dakota State University Fargo
摘要：Let X(nBAR) nBAR is-an-element-of N(d), be a field of independent real random variables, where N(d) is the d-dimensional lattice. In this paper, the law of the iterated logarithm is established for such a field of random variables. Theorem 1 brings into focus a connection between a certain strong law of large numbers and the law of the iterated logarithm. A general technique is developed by which one can derive the strong law of large numbers and the law of the iterated logarithm, exploiting t...
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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：PEMANTLE, R
作者单位：Cornell University
摘要：Consider a collection of real-valued random variables indexed the integers. It is well known that such a process can be stationary, that is, translation invariant, and ergodic and yet have very strong associations: The one-sided tail field may determine the sample; the measure may fail to be mixing in any sense; the weak law of large numbers may fail on some infinite subset of the integers. The main result of this paper is that this cannot happen if the integers are replaced by an infinite hom...
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作者：GRIFFIN, PS; MCCONNELL, TR
摘要：Let T(r) be the first time a sum S(n) of nondegenerate i.i.d. random vectors leaves the sphere of radius r. The spheres are determined by some given norm on R(d) which need not be the Euclidean norm. As a particular case of our results, we obtain, for mean-zero random vectors and each 0 < p < infinity and 0 less-than-or-equal-to q < infinity, necessary and sufficient conditions on the distribution of the summands to have E(parallel-to S(T(r))parallel-to - r)P = O(r(q)) as r --> infinity. We al...
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作者：LANDIM, C
摘要：We obtain the decay rate of the large deviation probabilities of occupation time for the symmetric simple exclusion process. Furthermore, in dimension d not-equal 2, we prove a large deviation principle for the occupation time. To obtain these results, we prove hydrodynamical limits for the weakly asymmetric simple exclusion process and we prove a large deviation principle for the empirical density for the symmetric simple exclusion process.
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作者：BERTOIN, J
摘要：If X is a spectrally positive Levy process, X(c)BAR the continuous part of its maximum process, and J the sum of the jumps of X across its previous maximum, then X - 2X(c)BAR - J has the same law as X conditioned to stay negative. This extends a result due to Pitman, who links the real Brownian motion and the three-dimensional Bessel process. Several other relations between the Brownian motion and the Bessel process are extended in this setting.
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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...
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作者：FITZSIMMONS, PJ; GETOOR, RK
摘要：We derive simple explicit formulas for the Fourier-Laplace transforms of the Hilbert transform and related functionals of the local time of a symmetric Levy process. These formulas generalize results of Biane and Yor for Brownian motion. The method of proof provides an explanation (of sorts) for the presence of the hyperbolic functions in such formulas.
