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作者：Adelman, O; Burdzy, K; Pemantle, R
作者单位：Sorbonne Universite; University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
摘要：A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability 1? Equivalently: three-dimensional Brownian motion hits any infinite cylinder with probability 1; does it hit all cylinders? This papers shows that the answer is no. Brownian motion in three dimensions avoids random cylinders and in fact avoids bodies of revolution that grow almost as fast as cones.
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作者：Choulli, T; Krawczyk, L; Stricker, C
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Marie et Louis Pasteur; University of Warsaw
摘要：After introducing a new concept, the notion of E-martingale, we extend the well-known Doob inequality (for 1 < p < + infinity) and the Burkholder-Davis-Gundy inequalities (for p = 2) to E-martingales. By means of these inequalities, we give sufficient conditions for the closedness of a space of stochastic integrals with respect to a fixed R-d-valued semimartingale, a question which arises naturally in the applications to financial mathematics. We also provide a necessary and sufficient conditi...
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作者：Adams, TM; Nobel, AB
作者单位：University System of Ohio; Ohio State University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider the problem of L-p-consistent density estimation from the initial segments of strongly dependent processes. It is shown that no procedure can consistently estimate the one-dimensional marginal density of every stationary ergodic process for which such a density exists. A similar result is established for the problem of estimating the support of the marginal distribution of an ergodic process.
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作者：Gadidov, A
作者单位：Gannon University
摘要：Let m greater than or equal to 2 be a nonnegative integer and let {X-(l), X-i((l))}(i) (is an element of) (N), l = 1,..., m, be m independent sequences of independent and identically distributed symmetric random variables. Define S-n = Sigma(1 less than or equal to 1, ... i) (m less than or equal to n) X-i1((1)) ... X-im((m)), and let {gamma(n)}(n is an element of N) be a nondecreasing sequence of positive numbers, tending to infinity and satisfying some regularity conditions. For m = 2 necess...
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作者：Bramson, M; Cox, JT; Durrett, RR
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Syracuse University; Cornell University; Cornell University
摘要：The voter model, with mutations occurring at a positive rate alpha, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d greater than or equal to 2. We show that, as alpha --> 0, the limiting distribution is right triangular in d = 2 and uniform in d greater than or equal to 3. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.
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作者：Piterbarg, VV
作者单位：University of Southern California
摘要：A sequence of piecewise constant approximations to rescaled isotropic homeomorphic stochastic flows is shown to converge weakly in Skorohod metric to the coalescing Brownian flow. Intermittent behavior of isotropic flows is exposed, and the clustering properties of isotropic flows are studied by the means of this convergence. We obtain qualitative and quantitative description of expansions and contractions of an arbitrary isotropic homeomorphic flow on large time- and space-scales.
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作者：Dawson, DA; Fleischmann, K; Leduc, G
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Quebec; University of Quebec Montreal
摘要：A general class of finite variance critical (xi, Phi, k)-superprocesses X in a Luzin space E with cadlag right Markov motion process xi, regular local branching mechanism Phi and branching functional k of bounded characteristic are shown to continuously depend on (Phi, k). As an application we show that the processes with a classical branching functional k(ds) = rho(s)(xi(s))ds [that is, a branching functional k generated by a classical branching rate rho(s)(gamma)] are dense in the above clas...
