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作者：WU, LM
作者单位：Wuhan University
摘要：This paper consists of three parts. In the first part, we find a common condition-the C-2-regularity-both for CLT and for moderate deviations. We show that this condition is verified in two important situations: the Lee-Yang theorem case and the FKG system case. In the second part; we apply the previous results to the additive functionals of a Markov process. By means of Feymman-Kac formula and Kato's analytic perturbation theory, we show that the Lee-Yang theorem holds under the assumption th...
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作者：DAWSON, DA; FLEISCHMANN, K; LI, Y; MUELLER, C
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Rochester
摘要：In a one-dimensional single point-catalytic continuous super-Brownian motion studied by Dawson and Fleischmann, the occupation density measure lambda(c) at the catalyst's position C is shown to be a singular (diffuse) random measure. The source of this qualitative new effect is the irregularity of the varying medium delta(c) describing the point catalyst. The proof is based on a probabilistic characterization of the law of the Palm canonical clusters chi appearing in the Levy-Khintchine repres...
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作者：DEHEUVELS, P; MASON, DM
作者单位：University of Delaware
摘要：We prove that the set of points where exceptional oscillations of empirical and related processes occur infinitely often is a random fractal, and evaluate its Hausdorff dimension.
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作者：BASS, RF; KHOSHNEVISAN, D
摘要：We give exact expansions for the upper and lower tails of the distribution of the maximum of local time of standard Brownian bridge on interval [0, 1]. We use the above expansions to prove upper and lower laws of the iterated logarithm for the maximum of the local time of the uniform empirical process. This solves two open problems cited in the book of Shorack and Wellner.
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作者：ALEXANDER, KS
摘要：The structure of a spanning forest that generalizes the minimal spanning tree is considered for infinite graphs with a value f(b) attached to each bond b. Of particular interest are stationary random graphs; examples include a lattice with lid uniform values f(b) and the Voronoi or complete graph on the sites of a Poisson process, with f(b) the length of b. The corresponding percolation models are Bernoulli bond percolation and the ''lily pad'' model of continuum percolation, respectively. It ...
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作者：BOLTHAUSEN, E; DEUSCHEL, JD; TAMURA, Y
作者单位：Technical University of Berlin; Keio University
摘要：We are investigating Markov process expectations for large time of the form exp(TF(L(T))), where L(T) is the empirical measure of a uniformly ergodic Markov process and F is a smooth functional. Such expressions are evaluated up to a factor which converges to 1. In contrast to earlier work on the subject, it is not assumed that the process is reversible.
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作者：PESZAT, S; ZABCZYK, J
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：It is shown that the transition semigroup (P-t)(t greater than or equal to 0) corresponding to a nonlinear stochastic evolution equation is strong Feller and irreducible, provided the nonlinearities are Lipschitz continuous and the diffusion term is nondegenerate. This result ensures the uniqueness of the invariant measure for (P-t)(t greater than or equal to 0).
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作者：ALGOET, PH
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作者：HAHN, MG; KLASS, MJ
作者单位：University of California System; University of California Berkeley; Tufts University
摘要：Let X(1),X(2),... be independent, mean zero, uniformly hounded random variables with S-n = X(1) +...+ X(n). Optimal criteria are determined on the length and location of an interval Gamma so that P(S-n epsilon Gamma) is proportional to (\Gamma\/root VarS(n)) boolean AND 1. The proof makes an unusual use of support considerations.
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作者：HAMMACK, W
摘要：We obtain a sharp probability bound on the maximal function of a strong subordinate of a bounded submartingale. An analogous inequality also holds for stochastic integrals in which the integrator is a bounded submartingale and the integrand is a bounded predictable process.
