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作者：Moynot, O; Samuelides, M
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; National Office for Aerospace Studies & Research (ONERA)
摘要：In this article, we study the asymptotic dynamics of a noisy discrete time neural network, with random asymmetric couplings and thresholds. More precisely, we focus our interest on the limit behaviour of the network when its size grows to infinity with bounded time. In the case of gaussian connection weights, we use the same techniques as Ben Arous and Guionnet (see [3]) to prove that the image law of the distribution of the neurons' activation states by the empirical measure satisfies a tempe...
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作者：Errami, M; Russo, F; Vallois, P
作者单位：Universite Paris 13; Universite de Lorraine
摘要：This article develops a framework of stochastic calculus with respect to a cadlag finite quadratic variation process. We apply it to the study of a generalization of a semi-martingale driven SDE studied by Kurtz, Pardoux and Protter [KPP]. We prove an Ito's formula for functions f(X) of a semimartingale with jumps when f has weak smoothness properties. Examples of X for which this formula is valid are time reversible semimartingales and solutions of [KPP] equations driven by Levy processes, pr...
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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：Johansson, K
作者单位：Royal Institute of Technology
摘要：We investigate certain measures induced by families of non-intersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have the same structure as the eigenvalue measures in random matrix theory like GUE, which can in fact can be obtained from non-intersecting Brownian motions. The derivations of the measures are based on the Karlin-Mc...
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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：Cavalier, L; Tsybakov, A
作者单位：Aix-Marseille Universite; Sorbonne Universite; Universite Paris Cite
摘要：We consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems, in particular multivariate ones. We propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale (that includes ellipoids with polynomially and exponentially decreasing axes) and, at the same time, satisfies asymptotically exact oracle inequalities within a...
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作者：Stannat, W
作者单位：University of Bielefeld
摘要：Let A be a Feller generator on a compact space and L be the corresponding Fleming-Viot (FV) operator with no selection and no recombination. In this paper we give conditions on A implying that the semigroup (T-t) generated by L (i) converges towards equilibrium with exponential rate (moreover, we determine explicit bounds on the rate of convergence in terms of A), (ii) is hypercontractive, (iii) is strong Feller, and (iv) is compact, We give applications of the last result to the existence of ...
