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作者：Burdzy, K; Chen, ZQ
作者单位：University of Washington; University of Washington Seattle
摘要：We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since it is not known whether a strong solution to the Skorohod equation in Lipschitz domains exists. Then we prove that the distance between the two processes converges to zero with probability one if the domain has a polygonal boundary or it is a lip domain, i.e., a domain betw...
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作者：Bougerol, P; Jeulin, T
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Baryshnikov [4] and Gravner, Tracy & Widom (15) have shown that the largest eigenvalue of a random matrix of the G.U.E. of order d has the same distribution as max(1greater than or equal tot1greater than or equal to...greater than or equal totd-1greater than or equal to0) [W-1(1) - W-1(t(1)) + W-2(t(1)) - W-2(t(2)) + ... + W-d(t(d-1))], where W = (W-1,...,W-d) is a d-dimensional Brownian motion. We provide a generalization of this formula to all the eigenvalues and give a geometric interpretat...
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作者：Chojnowska-Michalik, A; Goldys, B
作者单位：University of Lodz; University of New South Wales Sydney
摘要：We provide necessary and sufficient conditions for a Hilbert space-valued Ornstein-Uhlenbeck process to be reversible with respect to its invariant measure mu. For a reversible process the domain of its generator in L-p(mu) is characterized in terms of appropriate Sobolev spaces thus extending the Meyer equivalence of norms to any symmetric Ornstein-Uhlenbeck operator. We provide also a formula for the size of the spectral gap of the generator. Those results are applied to study the Ornstein-U...
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作者：Chen, ZQ; Kim, P
作者单位：University of Washington; University of Washington Seattle
摘要：Sharp two-sided estimates for Green functions of censored alpha-stable process Y in a bounded C-1.1 open set D are obtained, where alpha is an element of (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary partial derivativeD of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.
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作者：Burdzy, K; Nualart, D
作者单位：University of Washington; University of Washington Seattle; University of Barcelona
摘要：We study Brownian motion reflected on art independent Brownian path, We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain bounded by a Brownian path. We show that there exist two different natural local times for a Brownian path reflected on a Brownian path.
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作者：Handa, K
作者单位：Saga University
摘要：Fleming-Viot processes with mutation, selection and recombination are studied. Their reversible distributions are shown to he characterized as quasi-invariant measures with a cocycle given in terms of the mutation operator, the selection intensity, and the recombination kernel. By using this, we derive not only a necessary and sufficient condition for the Fleming-Viot process to he reversible, but also identify the reversible distributions in the reversible case.
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作者：Cattiaux, P; Mesnager, L
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre
摘要：Let L-1 = 1/2 Sigma(i.j=1)(d) a(ij)(t, x)partial derivative(i)partial derivative(j) + Sigma(i=1)(d) b(i)(t, x)partial derivative(i) = 1/2Sigma(j=1)(m) X-j(2) (t, x) + X-0(t, x) be a time dependent second order operator, written in usual or Hormander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process, under Hormander's like conditions. Coefficients are only Holder continuous in time. The main tool is Malliavin calculus. Our results exte...
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作者：Bendikov, A; Saloff-Coste, L
作者单位：Cornell University
摘要：Consider a central Gaussian convolution semigroup (mu(t))(t>0) on a connected compact semisimple group. Then either the measure mu(t) is singular with respect to Haar measure for all t > 0, or there exists a time t such that mu(t) is absolutely continuous with respect to Haar measure and admits a continuous density.
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作者：Mazza, C; Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：The well known convergence of the spectrum of large random symmetric matrices, due to Wigner, holds for products of correlated symmetric matrices with general entries. The limiting moments coincide with weighted enumeration of permutations, or of rooted trees. When the correlations are Markovian, the limiting first moments are closely related to Carlitz-Riordan q-Catalan numbers. As a consequence, these moments asymptotically exhibit a phase transition, with respect to the correlation coeffici...
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作者：Li, WBV; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let xi = (xi(i), 1 less than or equal to i less than or equal to n) and eta = (eta(t), 1 less than or equal to i less than or equal to n) be standard normal random variables with covariance matrices R-1 = (r(j,i)(1)) and R-0 = (r(j,i)(0)), resplectively, Slepian's lemma says that if r(j,i)(1) greater than or equal to r(j,i)(0) for 1 less than or equal to i, j less than or equal to n, the lower bound P (xi(t) < u for 1 <1 < n)/P(eta(i) less than or equal to u for 1 less than or equal to i less ...
