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作者：CHEN, X
摘要：In this paper we establish some general forms of the law of the iterated logarithm for independent random variables (X(n)) with Banach space values, where (X(n)) is not necessarily identically distributed. Our results include the Kolmogorov law of the iterated logarithm (LIL) in both finite and infinite dimensional cases, and they improve the Wittmann LIL as well as extend it to the vector setting. The Ledoux-Talagrand LIL for an i.i.d. sequence is also a simple corollary of our results.
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作者：NGUYEN, BG; YANG, WS
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：In this paper, we apply the Brydges-Spencer lace expansion and the Hara-Slade analysis to obtain the triangle condition for the nearest-neighbor oriented bond percolation in high dimensions and for the spread-out oriented bond percolation in Z(d) X Z, d greater than or equal to 5. Furthermore, we also establish the infrared bound in the subcritical region and the mean-field behavior for these models.
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作者：ROSINSKI, J; SAMORODNITSKY, G
作者单位：Cornell University
摘要：Subadditive functionals on the space of sample paths include suprema, integrals of paths, oscillation on sets and many others. In this paper we find an optimal condition which ensures that the distribution of a subadditive functional of sample paths of an infinitely divisible process belongs to the subexponential class of distributions. Further, we give exact tail behavior for the distributions of such functionals, thus improving many recent results obtained for particular forms of subadditive...
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作者：SZNITMAN, AS
作者单位：New York University
摘要：We consider Brownian motion evolving among killing traps. We develop a technique of ''enlargement of obstacles.'' This technique allows us to replace given trap configurations by configurations of enlarged traps, when deriving upper estimates on the probability that Brownian motion survives. Applied in a context of random obstacles, this reduces the complexity of the description for the environment seen by Brownian motion. We apply the method to the case where traps are distributed according t...
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作者：DILWORTH, SJ; MONTGOMERYSMITH, SJ
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Let X = Sigma epsilon(n)x(n) be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable parallel to X parallel to in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given.
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作者：CHANG, FC; KEMPERMAN, JHB; STUDDEN, WJ
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Let LAMBDA be the set of probability measures lambda on [0, 1]. Let M(n) = {(c1,..., c(n))\lambda is-an-element-of LAMBDA), where c(k) = c(k)(lambda) = integral-1/0x(k) dlambda, k = 1, 2,... are the ordinary moments, and assign to the moment space M(n) the uniform probability measure P(n). We show that, as n --> infinity, the fixed section (c1,..., c(k)), properly normalized, is asymptotically normally distributed. That is, square-root n[(c1,..., c(k)) - (c1(0),..., c(k)0] converges to MVN(0, ...
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作者：MYKLAND, PA
摘要：The paper contains a ''smoothed'' one-step triangular array asymptotic expansion for discrete-time martingales. An important element of the proof is a second-order description of Skorokhod embedding of discrete martingales in continuous ones. An application to Markov processes is given, along with a bootstrapping example.
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作者：BRADLEY, RC
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：For strictly stationary random fields indexed by R(d) or Z(d), certain versions of the ''strong mixing'' condition are equivalent to corresponding versions of the ''p-mixing'' condition.
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作者：KRONE, SM
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：In this work we study local times for a class of measure-valued Markov processes known as superprocesses. We begin by deriving analogues of well-known properties of ordinary local times. Then, restricting our attention to a class of superprocesses (which includes the important case of super-Brownian motion), we prove more detailed properties of the local times, such as joint continuity and a global Holder condition. These are then used to obtain path properties of the superprocesses themselves...
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作者：ANDJEL, ED
摘要：Bootstrap percolation is a model in which an element of Z2 becomes occupied in one time unit if two appropriately chosen neighbors are occupied. Schonmann [4] proved that starting from a Bernoulli product measure of positive density, the distribution of the time needed to occupy the origin decays exponentially. We show that for alpha > 1, the exponent can be taken as deltap2alpha for some delta > 0, thus showing that the associated characteristic exponent is at most two. Another characteristic...
