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作者：Bai, ZD
作者单位：National Sun Yat Sen University
摘要：It was conjectured in the early 1950's that the empirical spectral distribution of an n x n matrix, of lid entries, normalized by a factor of 1/root n, converges to the uniform distribution over the unit disc on the complex plane, which is called the circular law. Only a special case of the conjecture, where the entries of the matrix are standard complex Gaussian, is known. In this paper, this conjecture is proved under the existence of the sixth moment and some smoothness conditions. Some ext...
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作者：Kesten, H
作者单位：Cornell University
摘要：Let {X-i}(i greater than or equal to 1) be i.i.d. random variables with common distribution function F-1 and let S-n = Sigma(1)(n) X-i. We find a necessary and sufficient condition (directly in terms of Fl for the existence of sequences of constants (a,) and {beta(n)} with beta(n) up arrow infinity such that 0 < lim inf beta(n)(-1) max(j less than or equal to n) /S-j-alpha(j)/ < infinity w.p.1., and such that for any choice of <(alpha)over tilde>(n), it hold w.p.1 that lim inf beta(n)(-1) max(...
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作者：Wang, FY
作者单位：Beijing Normal University; University of Warwick
摘要：By using logarithmic transformations, an explicit lower bound estimate of heat kernels is obtained for diffusion processes on Riemannian manifolds. This estimate is sharp for both short and long times, especially for heat kernels on a compact manifold, and is extended to manifolds with unbounded curvature.
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作者：Haggstrom, O
作者单位：Chalmers University of Technology
摘要：We study dependent bond percolation on the homogeneous tree T-n of order n greater than or equal to 2 under the assumption of automorphism invariance. Excluding a trivial case, we find that the number of infinite clusters a.s. is either 0 or infinity. Furthermore, each infinite cluster a.s. has either 1, 2 or infinitely many topological ends, and infinite clusters with infinitely many topological ends have a.s. a branching,Umber greater than 1. We also show that if the marginal probability tha...
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作者：Rota, GC; Wallstrom, TC
作者单位：Massachusetts Institute of Technology (MIT); United States Department of Energy (DOE); Los Alamos National Laboratory; Catholic University of America
摘要：A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson-Charlier and Kravchuk polynomi...
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作者：Biggins, JD; Kyprianou, AE
作者单位：University of Sheffield
摘要：In the discrete-time supercritical branching random walk, there is a Kesten-Stigum type result for the martingales formed by the Laplace transform of the nth generation positions. Roughly, this says that for suitable values of the argument of the Laplace transform the martingales converge in mean provided an X log X condition holds. Here it is established that when this moment condition fails, so that the martingale converges to zero, it is possible to find a (Seneta-Heyde) renormalization of ...
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作者：Fannjiang, A; Komorowski, T
作者单位：University of California System; University of California Davis; Michigan State University
摘要：We study the asymptotic behavior of Brownian motion in steady, unbounded incompressible random flows. We prove an invariance principle for almost all realizations of random flows. The key compactness result is obtained by Moser's iterative scheme in PDE theory.
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作者：Zhang, LX
作者单位：Zhejiang University
摘要：Let (X-n; n greater than or equal to 0) be a sequence of random variables. We consider its geometrically weighted series xi(beta) = Sigma(n=0)(infinity) beta(n) X-n for 0 < beta < 1. This paper proves that xi(beta) can be approximated by Sigma(n=0)(infinity) beta(n) Y-n under some suitable conditions, where (Y-n; n greater than or equal to 0) is a sequence of independent normal random variables. Applications to the law of the iterated logarithm for xi(beta) are also discussed.
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作者：Protter, P; Talay, D
作者单位：Purdue University System; Purdue University; Inria
摘要：In relation with Monte Carlo methods to solve some integro-differential equations, we study the approximation problem of Eg(X-T) by Eg((X) over bar(T)(n)), where (X-t, 0 less than or equal to t less than or equal to T) is the solution of a stochastic differential equation governed by a Levy process (Z(t)), ((X) over bar(t)(n)) is defined by the Euler discretization scheme with step T/n. With appropriate assumptions on g(.), we show that the error Eg(X-T) - Eg((X) over bar(T)(n)) can be expande...
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作者：Krylov, NV
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Several stochastic partial differential equations are derived for multidimensional superdiffusions.
