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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：Götze, F; Tikhomirov, AN
作者单位：University of Bielefeld; Russian Academy of Sciences; Syktyvkar State University
摘要：We consider quadratic forms [GRAPHICS] where X-j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q(n), and the distribution of the same quadratic forms with X-j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well. as to nonstationary AR(1) processes.
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作者：Gyöngy, I; Nualart, D
作者单位：University of Edinburgh; University of Barcelona
摘要：In this paper we establish the existence and uniqueness of an L-2(R)-valued solution for a one-dimensional Burgers' equation perturbed by a space-time white noise on the real Line. We show that the solution is continuous in space and time, provided the initial condition is continuous. The main ingredients of the proof are maximal inequalities for the stochastic convolution, and some a priori estimates far a class of deterministic parabolic equations.
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作者：Albin, JMP; Leadbetter, MR
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We derive upper bounds for the conditional moment E{\ X \(e) \ Y = y} of a strictly alpha-stable random vector (X, Y) when alpha not equal 1 and rho less than or equal to 2 and prove weak convergence for the conditional law (X/u \ Y = u) as u --> infinity when alpha > 1. As an example of application, we derive a new result in crossing theory for ct-stable processes.
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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：van den Berg, J; Steif, JE
作者单位：Centrum Wiskunde & Informatica (CWI); Chalmers University of Technology
摘要：We study the existence of finitary codings (also called finitary homomorphisms or finitary factor maps) from a finite-valued i.i.d. process to certain random fields. For Markov random fields we show, using ideas of Marton and Shields, that the presence of a phase transition is an obstruction for the existence of the above coding; this yields a large class of Bernoulli shifts for which no such coding exists. Conversely, we show that, for the stationary distribution of a monotone exponentially e...
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作者：Delmas, JF; Dhersin, JS
作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Universite Paris Cite
摘要：We give a characterization of G-regularity for super-Brownian motion and the Brownian snake. More precisely, we define a capacity on E = (0, infinity) x R-d, which is not invariant by translation. We then prove that the measure of hitting a Borel set A subset of E for the graph of the Brownian snake excursion starting at (0, 0) is comparable, up to multiplicative constants, to its capacity. This implies that super-Brownian motion started at time 0 at the Dirac mass delta(0) hits immediately A ...
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作者：Millet, A; Sanz-Solé, M
作者单位：Sorbonne Universite; University of Barcelona; Universite Paris Nanterre
摘要：We prove the existence and uniqueness, for any time, of a real-valued process solving a nonlinear stochastic wave equation driven by a Gaussian noise white in time and correlated in the two-dimensional space variable. We prove that the solution is regular in the sense of the Malliavin calculus. We also give a decay condition on the covariance function of the noise under which the solution has Holder continuous trajectories and show that, under an additional ellipticity assumption, the law of t...
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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...
