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作者：HALL, P
摘要：Laws of the iterated logarithm are derived for row sums of triangular arrays of independent random variables, in the context of nonparametric regression estimators. These laws provide exact strong convergence rates for kernel type nonparametric regression estimators. They apply to the important case where design points are conditioned upon, and permit the design to be multivariate. We impose minimal conditions on the error distribution; in fact, only finite variance is needed.
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作者：MOUNTFORD, TS; PORT, SC
摘要：It is shown that all Levy processes on the line whose paths are of bounded variation have a closed range over any finite time interval that is nowhere dense except for those processes having positive (negative) drift with Levy measure finite on (0, infinity) [finite on (-infinity, 0)].
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作者：IOFFE, D
摘要：Two algorithms for calculating rate functions for a family of measures {mu-epsilon} on a B-space X are considered. The first one is a relaxed version of the Fenchel transform type theorem for convex rate functions. The second gives conditions under which {mu-epsilon} can be replaced by a more convenient family {mu-epsilon-x} near admissible points x is-an-element-of X such that rate functions for both families coincide near x. As an example, we apply both techniques to investigate large deviat...
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作者：SHEPP, L
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作者：BASS, RF; PEI, H
作者单位：Northwestern University
摘要：Bounds are found on the transition densities and Green functions for Brownian motion with normal reflection in Holder and Lipschitz domains. For Lipschitz domains, reflecting Brownian motion and boundary local time are constructed, a Harnack inequality valid up to the boundary is proved, a probabilistic solution to the Neumann problem is given and the Kuramochi boundary is identified.
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作者：DINWOODIE, IH
摘要：Let X(n)BAR denote the mean of an i.i.d. sequence of random vectors X1, X2, X3,... taking values in R(d). If lambda denotes the convex conjugate of the logarithm of the moment generating function for X1, then lim sup 1/n log P(X(n)BAR is-an-element-of C) less-than-or-equal-to -inf{lambda(upsilon): upsilon is-an-element-of C} when C subset-of R(d) is closed and the moment generating function for X1 is finite in a neighborhood of the origin. An example is given in which this upper bound fails fo...
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作者：DONNELLY, P
摘要：We derive conditions under which a sequence of processes will converge to a (continuous-time) Markov chain with an entrance boundary. Our main application of this result is in proving weak convergence of the so-called population ancestral processes, associated with a wide class of exchangeable reproductive models, to a particular death process with an entrance boundary at infinity. This settles a conjecture of Kingman. We also prove weak convergence of the absorption times of many neutral gene...
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作者：RACHEV, ST; RUSCHENDORF, L
作者单位：University of Munster
摘要：Let zeta be chosen at random on the surface of the p-sphere in R(n), Op,n : = {x is-an-element-of R(n): SIGMA-i = 1n \x(i)\p = n}. If p = 2, then the first k components zeta-1,...,zeta-k are, for k fixed, in the limit as n --> infinity independent standard normal. Considering the general case p > 0, the same phenomenon appears with a distribution F(p) in an exponential class E. F(p) can be characterized by the distribution of quotients of sums, by conditional distributions and by a maximum ent...
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作者：PAPAMARCOU, A; FINE, TL
作者单位：University System of Maryland; University of Maryland College Park; Cornell University
摘要：We discuss issues of existence and stochastic modeling in regard to sequences that exhibit combined features of independence and instability of relative frequencies of marginal events. The concept of independence used here is borrowed from the frequentist account of numerical probability advanced by von Mises: A sequence is independent if certain salient asymptotic properties are invariant under the causal selection of subsequences. We show that independence (in the above sense) and instabilit...
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作者：CHAVEL, I; FELDMAN, E; ROSEN, J
作者单位：City University of New York (CUNY) System; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：We define a renormalized intersection local time to describe the amount of self-intersection of the Brownian motion on a two-dimensional Riemannian manifold M. The second order asymptotics of the area of the Wiener sausage of radius epsilon on M are described in terms of the renormalized intersection local time.
