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作者：Bai, ZD; Silverstein, JW
作者单位：Northeast Normal University - China; North Carolina State University; National University of Singapore
摘要：Let B-n = (1/N)T-n(1/2) XnX*T-n(n)1/2 where X-n = (X-ij) is n x N with i.i.d. complex standardized entries having finite fourth moment, and T-n(1/2) is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. The limiting behavior, as n --> infinity with n/N approaching a positive constant, of functionals of the eigenvalues of B-n, where each is given equal weight, is studied. Due to the limiting behavior of the empirical spectral distribution of B,,, it is known that these li...
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作者：Jacod, J
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the Euler scheme for a stochastic differential equation driven by a Levy process Y. More precisely, we look at the asymptotic behavior of the normalized error process u(n) (X-n - X), where X is the true solution and X-n is its Euler approximation with stepsize 1/n, and u(n) is an appropriate rate going to infinity: if the normalized error processes converge, or are at least tight, we say that the sequence (u(n)) is a rate, which, in addition, is sharp when the limiting process (or pro...
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作者：Einmahl, U; Kuelbs, J
作者单位：Universite Libre de Bruxelles; University of Wisconsin System; University of Wisconsin Madison
摘要：Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related representation formula, and asymptotics for the integral term in this formula.
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作者：Abadi, M
作者单位：Universidade de Sao Paulo
摘要：We prove an upper bound for the error in the exponential approximation of the hitting time law of a rare event in alpha-mixing processes with exponential decay, phi-mixing processes with a summable function phi and for general psi-mixing processes with a finite alphabet. In the first case the bound is uniform as a function of the measure of the event. In the last two cases the bound depends also on the time scale t. This allows us to get further statistical properties as the ratio convergence ...
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作者：Chistyakov, GP; Götze, F
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：Let X, X-j, j is an element of N, be independent, identically distributed random variables with probability distribution F. It is shown that Student's statistic of the sample {X-j}(n)(j=1), has a limit distribution G such that G({-1, 1}) not equal 1, if and only if: (1) X is in the domain of attraction of a stable law with some exponent 0 < alpha less than or equal to 2; (2) EX = 0 if 1 < alpha < 2; (3) if alpha = 1, then X is in the domain of attraction of Cauchy's law and Feller's condition ...
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作者：Chen, DY; Peres, Y; Pete, G
作者单位：Peking University; University of California System; University of California Berkeley
摘要：Benjamini, Lyons and Schramm [Random Walks and Discrete Potential Theory (1999) 56-84] considered properties of an infinite graph G, and the simple random walk on it, that are preserved by random perturbations. In this paper we solve several problems raised by those authors. The anchored expansion constant is a variant of the Cheeger constant; its positivity implies positive lower speed for the simple random walk, as shown by Virag [Geom. Funct. Anal. 10 (2000) 1588-1605]. We prove that if G h...
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作者：Berti, P; Rigo, P
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：A notion of convergence in distribution for non (necessarily) measurable random elements, due to Hoffmann-Jorgensen, is characterized in terms of weak convergence of finitely additive probability measures. A similar characterization is given for a strengthened version of such a notion. Further, it is shown that the empirical process for an exchangeable sequence can fail to converge, due to the nonexistence of any measurable limit, although it converges for an i.i.d. sequence. Because of phenom...
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作者：Cerrai, S; Röckner, M
作者单位：University of Florence; University of Bielefeld
摘要：Following classical work by Freidlin [Trans. Amer Math. Soc. (1988) 305 665-657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504-537] and Peszat [Probab. Theory Related Fields (1994) 98 113-136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction-diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results...
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作者：Chen, ZQ; Fitzsimmons, PJ; Takeda, M; Ying, J; Zhang, TS
作者单位：University of Washington; University of Washington Seattle; Tohoku University; University of California System; University of California San Diego; Fudan University; University of Manchester
摘要：We study Girsanov's theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of gradient type. We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the case of processes with jumps.
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作者：Funaki, T
作者单位：University of Tokyo
摘要：We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a > 0. We say a chain is formed when the particles are arranged in an almost equal distance a. If a chain is formed at time 0, so is for positive time as the temperature of the system decreases to 0 and, under a suitable macroscopic space-time scaling, the center of mass of the chain pe...
