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作者：Nualart, D; Rovira, C; Tindel, S
作者单位：University of Barcelona; Universite Paris 13
摘要：We consider a vortex structure based on a three-dimensional fractional Brownian motion with Hurst parameter H > (1)/(2). We show that the energy H has moments of any order under suitable conditions. When H epsilon ((1)/(2), (1)/(3)) we prove that the intersection energy H-xy can be decomposed into four terms, one of them being a weighted self-intersection local time of the fractional Brownian motion in R-3.
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作者：Da Prato, G; Debussche, A
作者单位：Scuola Normale Superiore di Pisa
摘要：We prove the existence and uniqueness of a strong solution of the stochastic quantization equation in dimension 2 for almost all initial data with respect to the invariant measure. The method is based on a fixed point result in suitable Besov spaces.
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作者：van der Hofstad, R; den Hollander, F; König, W
作者单位：Eindhoven University of Technology; Technical University of Berlin
摘要：In this article, we prove a large deviation principle for the empirical drift of a one-dimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers and a central limit theorem were derived. In the Edwards model, a path of length T receives a penalty e-(betaHT), where H-T is the self-intersection local time of the path and P E (0, 00) is a parameter called the strength of self-repellence. We identify the rate function...
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作者：Gradinaru, M; Russo, F; Vallois, P
作者单位：Universite de Lorraine; Universite Paris 13
摘要：Given a locally bounded real function g, we examine the existence of a 4-covariation [g(B-H), BH, BH, BH], where BH is a fractional Brownian motion with a Hurst index H greater than or equal to (1)/(4). We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case H = (1)/(4), generalizing an identity of Bouleau-Yor type, well known for the classical Brownian motion. A second application is an Ito formula of Stra...
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作者：Revelle, D
作者单位：University of California System; University of California Berkeley
摘要：This article examines the rate of escape for a random walk on G Z and proves laws of the iterated logarithm for both the inner and outer radius of escape. The class of G for which these results hold includes finite, G as well as groups of the form H Z, so the construction can be iterated. Laws of the iterated logarithm are also found for random walk on Baumslag-Solitar groups and a discrete version of the Sol geometry.
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作者：Klüppelberg, C; Pergamenchtchikov, S
作者单位：Technical University of Munich; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten [Ann. Probab. 2 (1974) 355-386]. Compactness of the state space and a certain continuity condition allows us to simplify Kesten's proof considerably.
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作者：Reitzner, M
作者单位：Technische Universitat Wien; University of Freiburg
摘要：Let K be a smooth convex body. The convex hull of independent random points in K is a random polytope. Estimates for the variance of the volume and the variance of the number of vertices of a random polytope are obtained. The essential step is the use of the Efron-Stein jackknife inequality for the variance of symmetric statistics. Consequences are strong laws of large numbers for the volume and the number of vertices of the random polytope. A conjecture of Barany concerning random and best-ap...
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作者：Roos, B
作者单位：University of Hamburg
摘要：We consider the approximation of the distribution of the sum of independent but not necessarily identically distributed random variables by a compound Poisson distribution and also by a finite signed measure of higher accuracy. Using Kerstan's method, some new bounds for the total variation distance are presented. Recently, several authors had difficulties applying Stein's method to the problem given. For instance, Barbour, Chen and Loh used this method in the case of random variables on the n...
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作者：Benjamini, I; Kalai, G; Schramm, O
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; Microsoft
摘要：Let 0 < a < b < infinity, and for each edge e of Z(d) let omega(e) = a or omega(e) = b, each with probability 1/2, independently. This induces a random metric dist(omega) on the vertices of Zd, called first passage percolation. We prove that for d > 1, the distance dist(omega)(0, v) from the origin to a vertex v, \v\ > 2, has variance bounded by C\v\/log \v\, where C = C(a, b, d) is a constant which may only depend on a, b and d. Some related variants are also discussed.
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作者：Brofferio, S
作者单位：Graz University of Technology
摘要：The auto-regressive model on R-d defined by the recurrence equation Y-n(y) = a(n)Y(n-1)(y) + B-n, where {(a(n), B-n)}(n) is a sequence of i.i.d. random variables in R+* x R-d, has, in the r=critical case E[loga(1)] = 0, a local contraction property, that is, when Y-n(y) is in a compact set the distance \Y-n(y) - Y-n(x)\ converges almost surely to 0. We determine the speed of this convergence and we use this asymptotic estimate to deal with some higher-dimensional situations. In particular, we ...
