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作者：Wang, QY; Jing, BY; Zhao, LC
作者单位：University of Wollongong; Hong Kong University of Science & Technology; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：We derive Berry-Esseen bounds for a class of Studentized statistics. The results are applied to Studentized U-statistics, Studentized L-statistics and Studentized functions of the sample mean to give the Berry-Esseen bounds under conditions weaker than those obtained by alternative methods.
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作者：Dembo, A; Peres, Y; Rosen, J; Zeitouni, O
作者单位：Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; Technion Israel Institute of Technology
摘要：Let F(x, r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in R-3. We prove that sup(\x\less than or equal to 1) F(x, r)/(r(2) \log r\) --> 16/pi(2) a.s. as r --> 0, thus solving a problem posed by Taylor in 1974. Furthermore, for any a epsilon (0, 16/pi(2)), the Hausdorff dimension of the set of thick points x for which lim sup(r-->0) F(x, r)/(r(2)\log r\) = a is almost surely 2 - a pi(2)/8; this is the correct scaling to obtain a nondegenerate m...
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作者：Samson, PM
作者单位：Universite de Toulouse
摘要：We prove concentration inequalities for some classes of Markov chains and Phi-mixing processes, with constants independent of the size of the sample, that extend the inequalities for product measures of Talagrand. The method is based on information inequalities put forward by Marton in case of contracting Markov chains. Using a simple duality argument on entropy, our results also include the family of logarithmic Sobolev inequalities for convex functions. Applications to bounds on supremum of ...
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作者：Chen, X; Kuelbs, J; Li, WB
作者单位：Northwestern University; University of Wisconsin System; University of Wisconsin Madison; University of Delaware
摘要：A functional law of the iterated logarithm is obtained for symmetric stable processes with stationary independent increments. This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion. Proofs depend on small ball probability estimates and yield the small ball probabilities of the weighted sup-norm for these processes.
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作者：Cox, JT; Durrett, R; Perkins, EA
作者单位：Syracuse University; Cornell University; University of British Columbia
摘要：We show that a sequence of voter models, suitably rescaled in space and time, converges weakly to super-Brownian motion. The result includes both nearest neighbor and longer range voter models and complements a limit theorem of Mueller and Tribe in one dimension.
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作者：Chiang, TS; Sheu, SJ
作者单位：Academia Sinica - Taiwan
摘要：where b is smooth except possibly along the hyperplane x(1) = 0, we shall consider the large deviation principle for the law of the solution diffusion process and its occupation time as epsilon --> 0. In other words, we consider P(\\X-epsilon - phi\\ < delta, \\u(epsilon) - psi\\ < delta) where u(epsilon)(t) and psi(t) are the occupation times of XE and cp in the positive half space {x epsilon R-d: x(1) > 0}, respectively. As a consequence, an unified approach of the lower level large deviatio...
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作者：Tolmatz, L
作者单位：Southern Illinois University System; Southern Illinois University
摘要：The distribution of the integral of the absolute value of the Brownian bridge was expressed by Cifarelli and independently by Johnson and Killeen in the form of a series. Rice obtained the corresponding probability density by numerical integration. Here we determine the exact tail asymptotics of this distribution, as well as the exact asymptotics of its density function for the large values of the argument.
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作者：Nualart, D; Viens, F
作者单位：University of Barcelona; University of North Texas System; University of North Texas Denton
摘要：We study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup, whose kernel p(s, t, y, x) is Brownian in s and t. The kernel p is supposed to be measurable with respect to the increments of an underlying Wiener process in the interval [s, t]. The evolution equation is then anticipative and, choosing the Skorohod formulation, we establish existence and uniqueness of a continuous solution with values in L-2(R-d). As an ap...
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作者：Puha, AL
作者单位：California State University System; California State University San Marcos
摘要：The uniform model is a reversible interacting particle system that evolves on the homogeneous tree. Occupied sites become vacant at rate one provided the number of occupied neighbors does not exceed one. Vacant sites become occupied at rate beta times the number of occupied neighbors. On the binary tree, it has been shown that the survival threshold beta(c) is 1/4. In particular, for beta less than or equal to 1/4, the expected extinction time is finite. Otherwise, the uniform model survives l...
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作者：Verzani, J; Adler, R
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
摘要：We construct a super iterated Brownian motion (SIBM) from a historical version of iterated Brownian motion (IBM) using an iterated Brownian snake (IBS). It is shown that the range of super iterated Brownian motion is qualitatively quite different from that of super Brownian motion in that there are points with explosions in the branching. However, at a fixed time the support of SIBM has an exact Hausdorff measure function that is the same (up to a constant) as that of super Brownian motion at ...
