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作者：Chen, ZQ; Durrett, R; Ma, G
作者单位：Cornell University
摘要：We study a family of differential operators (L-alpha, alpha greater than or equal to 0) in the unit bah D of C-n with n greater than or equal to 2 that generalize the classical Laplacian, alpha = 0, and the conformal Laplacian, alpha = 1/2 (that is, the Laplace-Beltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of L-alpha-harmonic functions is studied in a unified way for 0 less than or equa...
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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 give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semiflow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate <(lambda)over bar>(1) (sigma) of the trajectories expressed in terms of the noise variance sigma. Roughly speaking we show that for small sigma, <(lambda)over bar>(...
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作者：Donati-Martin, C; Yor, M
作者单位：Sorbonne Universite
摘要：We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob's h-transforms of Brownian motion, for nonpositive harmonic functions h. We also give a survey and complement some martingale approaches to Ray-Knight theorems for local times.
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作者：Latala, R
作者单位：University of Warsaw
摘要：For the sum S = Sigma X-i of a sequence (X-i) of independent symmetric (or nonnegative) random variables, we give lower and upper estimates of moments of S. The estimates are exact, up to some universal constants, and extend the previous results for particular types of variables X-i.
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作者：Gine, E; Gotze, F; Mason, DM
作者单位：University of Connecticut; University of Connecticut; University of Bielefeld; University of Delaware
摘要：Let X, X-i, i is an element of N, be independent, identically distributed random variables. It is shown that the Student t-statistic based upon the sample {X-i}(i less than or equal to 1)(n) is asymptotically N(0, 1) if and only if X is in the domain of attraction of the normal law. It is also shown that, for any X, if the self-normalized sums U-n := Sigma(i=1)(n) X-i/(Sigma(i=1)(n) X-i(2))(1/2), n is an element of N, are stochastically bounded then they are uniformly subgaussian that is, sup(...
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作者：Darling, RWR; Pardoux, E
作者单位：State University System of Florida; University of South Florida; Aix-Marseille Universite
摘要：Suppose {T-t} is the filtration induced by a Wiener process W in R-d, tau is a finite {T-t} stopping time (terminal time), xi is an T-tau-measurable random variable in R-k (terminal value) and f(., y, z) is a coefficient process, depending on y is an element of R-k and z is an element of L(R-d; R-k), satisfying (y - (y) over bar) [f(s, y, z) - f(s, (y) over bar, z)] less than or equal to -a/y - (y) over bar/(2) (f need not be Lipschitz in Y), and /f(s, y, z) -f(s, y (z) over bar/ less than or ...
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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：Liao, M
作者单位：Auburn University System; Auburn University
摘要：We obtain a formula for Lyapunov exponents of stochastic flows generated by stochastic differential equations on compact manifolds. As an application, the exponents of a class of stochastic flows on spheres are determined explicitly.
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作者：Sznitman, AS
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We describe a coarse graining method, which provides lower bounds on the principal Dirichlet eigenvalue of the Laplacian in regions receiving small obstacles, and sharpens the previous method of enlargement of obstacles. Based on a quantitative Wiener criterion, one replaces the actual obstacles by obstacles of a much larger size. Controls on the shift of principal eigenvalues and capacity estimates on the locus where the Wiener criterion breaks down are derived. The results are written in a s...
