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作者：Davis, RA; Mikosch, T
作者单位：Colorado State University System; Colorado State University Fort Collins; University of Groningen
摘要：It is a well-known fact that the periodogram ordinates of an lid mean-zero Gaussian sequence at the Fourier frequencies constitute an lid exponential vector, hence the maximum of these periodogram ordinates has a limiting Gumbel distribution. We show for a non-Gaussian lid mean-zero, finite variance sequence that this statement remains valid. We also prove that the point process constructed from the periodogram ordinates converges to a Poisson process. This implies the joint weak convergence o...
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作者：Janvresse, E; Landim, C; Quastel, J; Yau, HT
作者单位：Centre National de la Recherche Scientifique (CNRS); New York University; University of Toronto
摘要：Under mild assumptions we prove that for any local function u the decay rate to equilibrium in the variance sense of zero range dynamics on the d-dimensional integer lattice is C(u)t(-d/2) + o(t(-d/2)). The constant C-u is computed explicitly.
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作者：Zhang, CH
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：This paper concerns moment and tail probability inequalities and the strong law of large numbers for U-statistics with nonnegative or symmetrized kernels and their multisample and decoupled versions. Sub-Bernoulli functions are used to obtain the moment and tail probability inequalities, which are then used to obtain necessary and sufficient conditions for the almost sure convergence to zero of normalized U-statistics with nonnegative or completely symmetrized kernels, without further regulari...
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作者：Donnelly, P; Kurtz, TG
作者单位：University of Oxford; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：Models of populations in which a type or location, represented by a point in a metric space E, is associated with each individual in the population are considered. A population process is neutral if the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models, and it is shown that these measure-valued processes can be represented in terms of the total mass of the p...
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作者：Arnold, L; Imkeller, P
作者单位：University of Bremen; Humboldt University of Berlin
摘要：Let dx = Sigma(i=0)(m) A(i)x circle dW(i) be a linear SDE in R-d, generating the flow Phi(t), of Linear isomorphisms. The multiplicative ergodic theorem asserts that every vector v is an element of R-d \ {0} possesses a Lyapunov exponent (exponential gran th rate) lambda(v) under Phi(t), which is a random variable taking its values from a finite list of canonical exponents lambda(i) realized in the invariant Oseledets spaces E-i. We prove that, in the case of simple Lyapunov spectrum, every 2-...
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作者：Handjani, SJ
作者单位：University of Mississippi
摘要：We consider the d-dimensional threshold voter model. It is known that, except in the one-dimensional nearest-neighbor case, coexistence occurs (nontrivial invariant measures exist). In fact, there is a nontrivial limit eta(infinity)(1/2) Obtained by starting from the product measure with density 1/2. We show that in these coexistent cases, eta(t) double right arrow alpha delta(0) + beta delta(1) (1- alpha - beta)eta(infinity)(1/2) as t --> infinity, where alpha = P(tau(0) < infinity), beta = P...
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作者：Boucher, C; Ellis, RS; Turkington, B
作者单位：Illinois Wesleyan University; University of Massachusetts System; University of Massachusetts Amherst
摘要：The main theorem is the large deviation principle for the doubly indexed sequence of random measures [GRAPHICS] Here theta is a probability measure on a Polish space K, {D-r, k, k = 1,...,2(r)} is a dyadic partition of K (hence the use of 2(r) summands) satisfying theta{D-r,D-k} = 1/2(r) and L-q,(1), L-q,(2),...,L-q, (2r) is an independent, identically distributed sequence of random probability measures on a Polish space Y such that {L-q,L-k, q is an element of N} satisfies the large deviation...
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作者：Marsalle, L
作者单位：Sorbonne Universite
摘要：Let L be a local time. It is well known that there exist a law of the iterated logarithm and a modulus of continuity for L. Motivated by the case of real Brownian motion, we study the existence of fast points and slow points of L. We prove the existence of such points by considering the right-continuous inverse of L, which is a subordinator.
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作者：Bentkus, V; Götze, F
作者单位：University of Bielefeld
摘要：Let X, X-1, X-2,... be i.i.d. random variables taking values in a measurable space H. Let phi(x, y) and phi(1)(x) denote measurable functions of the arguments x, y is an element of H. Assuming that the kernel phi is symmetric and that E phi(x, X) = 0, for all x, and E phi(1)(X) = 0, we consider U-statistics of type [GRAPHICS] It is known that the conditions E phi(2)(X, X-1) < infinity and E phi(1)(2)(X) < infinity imply that the distribution function of T, say F, has a limit, say F-0, which ca...
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作者：de la Peña, VH
作者单位：Columbia University
摘要：In this paper we introduce a technique for obtaining exponential inequalities, with particular emphasis placed on results involving ratios. Our main applications consist of approximations to the tail probability of the ratio of a martingale over its conditional variance (or its quadratic variation for continuous martingales). We provide examples that strictly extend several of the classical exponential inequalities for sums of independent random variables and martingales. The spirit of this ap...
