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作者：Hu, Yaozhong; Nualart, David
作者单位：University of Kansas
摘要：The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (0,1) in time. Two types of equations are considered. First we consider the equation in the Ito-Skorohod sense, and later in the Stratonovich sense. An explicit chaos expansion for the solution is obtained. On the other hand, the moments of the solution are express...
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作者：Talagrand, Michel
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：Given numbers a(ij) >= 0 for 1 <= i < j <= N, and given numbers b(i) >= 0, i <= N, we consider the random Hamiltonian Sigma(i, j <= N) root a(ij)g(ij)sigma(i)sigma(j) + Sigma(i <= N) root b(i)g(i)sigma(i), where g(i), g(ij) denote independent standard normal r.v., and where sigma(i) = +/- 1. We give sufficient conditions on the coefficients a(ij) for the system governed by this Hamiltonian to exhibit high-temperature behavior. There results extend known facts concerning the behavior of the She...
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作者：Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulalia
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; Universite Paris 13
摘要：We consider a system of d non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional space-time white noise. The non-linearities appear both as additive drift terms and as multipliers of the noise. Using techniques of Malliavin calculus, we establish upper and lower bounds on the one-point density of the solution u(t, x), and upper bounds of Gaussian-type on the two-point density of (u(s, y), u(t, x)). In particular, this estimate quantifies how this density degenerate...
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作者：Mueller, Ursula U.; Schick, Anton; Wefelmeyer, Wolfgang
作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; Texas A&M University System; Texas A&M University College Station; University of Cologne
摘要：We prove a Bahadur representation for a residual-based estimator of the innovation distribution function in a nonparametric autoregressive model. The residuals are based on a local linear smoother for the autoregression function. Our result implies a functional central limit theorem for the residual-based estimator.
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作者：Greven, Andreas; Pfaffelhuber, Peter; Winter, Anita
作者单位：University of Erlangen Nuremberg; University of Freiburg
摘要：We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all finite subspaces sampled from these spaces converge. This topology is metrized following Gromov's idea of embedding two metric spaces isometrically into a common metric space combined with the Prohorov metric between probability measures on a fixed metric space....
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作者：Chen, Lung-Chi; Sakai, Akira
作者单位：Hokkaido University; Fu Jen Catholic University
摘要：We prove that the Fourier transform of the properly scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index alpha > 0 converges to e(-C)vertical bar k vertical bar(alpha boolean AND 2) for some C is an element of (0, infinity) above the upper- critical dimension d(c) equivalent to 2(alpha boolean AND 2). This answers the open question remained in the previous paper (Chen and Sakai in Probab Theory Relat Fields 142:151-188, 2008). Moreover, we...
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作者：Guillin, Arnaud; Leonard, Christian; Wu, Liming; Yao, Nian
作者单位：Aix-Marseille Universite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
摘要：chi chi chi In this paper, one investigates the transportation-information TcI inequalities: alpha(T-c(nu, mu)) <= I(nu vertical bar mu) for all probability measures nu on a metric space (X, d), where mu is a given probability measure, T-c(nu, mu) is the transportation cost from nu to mu with respect to the cost function c(x, y) on X-2, I(nu vertical bar mu) is the Fisher-Donsker-Varadhan information of nu with respect to mu and alpha : [0, infinity) -> [0, infinity] is a left continuous incre...
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作者：Brzezniak, Zdzislaw; Hausenblas, Erika
作者单位：University of York - UK; Salzburg University
摘要：We generalize the maximal regularity result from Da Prato and Lunardi (Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei (9) Mat Appl 9(1):25-29, 1998) to stochastic convolutions driven by time homogenous Poisson random measures and cylindrical infinite dimensional Wiener processes.
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作者：Borodin, Alexei; Olshanski, Grigori
作者单位：California Institute of Technology; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n -> az, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.
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作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.
