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作者：Schechtman, G; Schlumprecht, T; Zinn, J
作者单位：Weizmann Institute of Science; Texas A&M University System; Texas A&M University College Station
摘要：The Gaussian correlation conjecture states that for any two symmetric, convex sets in n-dimensional space and for any centered, Gaussian measure on that space, the measure of the intersection is greater than or equal to the product of the measures. In this paper we obtain several results which substantiate this conjecture. For example, in the standard Gaussian case, we show there is a positive constant, c, such that the conjecture is true if the two sets are in the Euclidean ball of radius c r...
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作者：Dalang, RC; Frangos, NE
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Athens University of Economics & Business
摘要：We consider the wave equation in two spatial dimensions driven by space-time Gaussian noise that is white in time but has a nondegenerate spatial covariance. We give a necessary and sufficient integral condition on the covariance function of the noise for the solution to the linear form of the equation to be a real-valued stochastic process, rather than a distribution-valued random variable. When this condition is satisfied, we show that not only the linear form of the equation, but also nonli...
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作者：Duheille, F
作者单位：Universite Claude Bernard Lyon 1
摘要：We prove that, under some general assumptions, the range of any nonconstant harmonic morphism from a simply connected open set U in R-n to R-3, n > 3, cannot avoid three concurrent half-lines, which is an extension to Picard's little theorem. To this end, we will prove two results concerning the windings of Brownian motion around three concurrent half-lines in R-3 and the recurrence of some domains linked with the harmonic morphism.
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作者：Aaronson, J; Denker, M
作者单位：Tel Aviv University; University of Gottingen
摘要：The domain of attraction of a 1-stable law on R-d is characterized by the expansions of the characteristic functions of its elements.
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作者：Sturm, KT
作者单位：University of Bonn
摘要：We present a general method to construct m-symmetric diffusion processes (X-t,P-x) on any given locally compact metric space (X,d) equipped with a Radon measure m. These processes are associated with local regular Dirichlet forms which are obtained as Gamma-limits of approximating nonlocal Dirichlet forms. This general method works without any restrictions on (X, d, m) and yields processes which are well defined for quasi every starting point. The second main topic of this paper is to formulat...
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作者：Jacod, J; Protter, P
作者单位：Sorbonne Universite; Purdue University System; Purdue University
摘要：We are interested in the rate of convergence of the Euler scheme approximation of the solution to a stochastic differential equation driven by a general (possibly discontinuous) semimartingale, and by the asymptotic behavior of the associated normalized error. It is well known that for Ito's equations the rate is 1/root n;we provide a necessary and sufficient condition for this rate to be 1 root n when the driving semimartingale is a continuous martingale, or a continuous semimartingale under ...
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作者：Mohammed, SEA; Scheutzow, MKR
作者单位：Southern Illinois University System; Southern Illinois University; Technical University of Berlin
摘要：We study the behavior for large \x\ of Kunita-type stochastic flows phi(t, omega, x) on R-d, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large \x\, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential ...
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作者：Grigor'yan, A; Kelbert, M
作者单位：Imperial College London
摘要：We investigate the escape rate of the Brownian motion W-x(t) on a complete noncompact Riemannian manifold. Assuming that the manifold has at most polynomial volume growth and that its Ricci curvature is bounded below, we prove that dist(W-x(t), x) less than or equal to root Ct log t for all large t with probability 1. On the other hand, if the Ricci curvature is nonnegative and the volume growth is at least polynomial of the order n > 2, then dist(W-x(t), x) greater than or equal to root Ct/lo...
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作者：Wehr, J; Woo, J
作者单位：University of Arizona; University of Arizona
摘要：An H-geodesic is a doubly infinite path which locally minimizes the passage time in the i.i.d. first passage percolation model on a half-plane H. Under the assumption that the bond passage times are continuously distributed with a finite mean, we prove that, with probability 1, H-geodesics do not exist. As a corollary we show that, with probability 1, any geodesic in the analogous model on the whole plane Z(2) has to intersect all straight lines with rational slopes.
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作者：Hambly, BM; Lyons, TJ
作者单位：University of Edinburgh; Imperial College London
摘要：We construct a Levy stochastic area for Brownian motion on the Sierpinski gasket. The standard approach via Ito integrals fails because this diffusion has sample paths which are far rougher than those of semimartingales. We thus provide an example demonstrating the restrictions of the semimartingale framework. As a consequence of the existence of the area one has a stochastic calculus and can solve stochastic differential equations driven by Brownian motion on the Sierpinski gasket.
