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作者：Duvillard, TC; Guionnet, A
作者单位：Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Using It (o) over caps calculus, we study the large deviations properties of the law of the spectral measure of the Hermitian Brownian motion. We extend this strategy to the symmetric, unitary and Wishart processes. This dynamical approach is generalized to the study of the large deviations of the non-commutative laws of several independent Hermitian Brownian motions. As a consequence, we can bound from above entropies defined in the spirit of the microstates entropy introduced by Voiculescu.
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作者：Goldie, CM; Maller, RA
作者单位：University of Sussex; University of Western Australia
摘要：For a series of randomly discounted terms we give an integral criterion to distinguish between almost-sure absolute convergence and divergence in probability to infinity, these being the only possible forms of asymptotic behavior. This solves the existence problem for a one-dimensional perpetuity that remains from a 1979 study by Vervaat, and yields a complete characterization of the existence of distributional fixed points of a random affine map in dimension one.
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作者：Sethuraman, S
作者单位：Iowa State University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Some invariance principles for additive functionals of simple exclusion with finite-range translation-invariant jump rates p(i, j) = p(j - i) in dimensions d greater than or equal to 1 are established. A previous investigation concentrated on the case of p symmetric. The principal tools to take care of nonreversibility, when p is asymmetric, are invariance principles for associated random variables and a local balance estimate on the asymmetric generator of the process. As a by-product, we pro...
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作者：Higuchi, Y; Zhang, Y
作者单位：Kobe University; University of Colorado System; University of Colorado at Colorado Springs
摘要：Consider first passage Ising percolation on Z(2). Let beta denote the reciprocal temperature and let h denote an external magnetic field. Denote by beta(c) the critical temperature and, for beta < beta(c), let h(c)(beta)= h(c) = sup{h: theta(beta, h) = 0}, where theta(beta, h) is the probability that the origin is connected by an infinite (+)-cluster. With these definitions let us consider first passage Ising percolation on Z(2). Let a(0,n) denote the first passage time from (0, 0) to (n, 9). ...
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作者：Van den Berg, J; Kesten, H
作者单位：Cornell University
摘要：We consider a system of particles, each of which performs a continuous time random walk on Z(d). The particles interact only at times when a particle jumps to a site at which there are a number of other particles present. If there are j particles present, then the particle which just jumped is removed from the system with probability p(j). We show that if p(j) is increasing in j and if the dimension d is at least 6 and if we start with one particle at each site of Z(d), then p(t) := P{there is...
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作者：Athreya, S; Tribe, R
作者单位：University of British Columbia; University of Warwick
摘要：We establish a duality relation for the moments of bounded solutions to a class of one-dimensional parabolic stochastic partial differential equations. The equations are driven by multiplicative space-time white noise, with a non-Lipschitz multiplicative functional. The dual process is a system of branching Brownian particles. The same method can be applied to show uniqueness in law for a class of non-Lipschitz finite dimensional stochastic differential equations.
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作者：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; Lund University
摘要：Let B be a Banach space and F any family of bounded linear functionals on B of norm at most one. For x is an element of B set \\X\\ = sup(Lambda is an element ofF) Lambda>(*) over bar * (x) (\\.\\ is at least a seminorm on B), We give probability estimates for the tail probability of S-n* = max(1 less than or equal tok less than or equal ton) \\Sigma (k)(j=1) X-j\\ where {X-i}(i=1)(n) are independent symmetric Banach space valued random elements. Our method is based on approximating the probab...
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作者：Surgailis, D
作者单位：Vilnius University
摘要：We study limit distributions of sums S-N((G)) = Sigma(t=1)(N) G(X-t) of nonlinear functions G(x) in stationary variables of the form X-t = Y-t + Z(t), where {Y-t} is a linear (moving average) sequence with long-range dependence, and {Z(t)} is a (nonlinear) weakly dependent sequence. In particular, we consider the case when {Y-t} is Gaussian and either (1) {Z(t)} is a weakly dependent multilinear form in Gaussian innovations, or (2) {Z(t)} is a finitely dependent functional in Gaussian innovati...
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作者：Mikosch, T; Resnick, S; Samorodnitsky, G
作者单位：University of Groningen; Cornell University
摘要：We consider the maximum of the periodogram based on an infinite variance heavy-tailed sequence. For alpha < 1 we show that the maxima constitute a weakly convergent sequence and find its limiting distribution. For 1 alpha < 2 we show that the sequence of the maxima is not tight and find a normalization that makes it tight.
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作者：Nishiyama, Y
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This paper deals with weak convergence of stochastic integrals with respect to multivariate point processes. The results are given in terms of an entropy condition for partitioning of the index set of the integrands, which is a sort of L-2-bracketing. We also consider l(infinity)-valued martingale difference arrays, and present natural generalizations of Jain-Marcus's and Ossiander's central limit theorems. As an application, the asymptotic behavior of log-likelihood ratio random fields in gen...
