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作者：Heinrich, M; Rolles, SWW
作者单位：University of Bielefeld; University of California System; University of California Los Angeles
摘要：We show that an i.i.d. uniformly colored scenery on Z observed along a random walk path with bounded jumps can still be reconstructed if there are some errors in the observations. We assume the random walk is recurrent and can reach every point with positive probability. At time k, the random walker observes the color at her present location with probability 1 - delta and an error Y-k with probability delta. The errors Y-k, k greater than or equal to 0, are assumed to be stationary and ergodic...
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作者：Li, XD
作者单位：University of Oxford
摘要：We introduce Sobolev spaces and capacities on the path space P-m0 (M) over a compact Riemannian manifold M. We prove the smoothness of the Ito map and the stochastic anti-development map in the sense of stochastic calculus of variation. We establish a Sobolev norm comparison theorem and a capacity comparison theorem between the Wiener space and the path space P-m0 (M). Moreover, we prove the tightness of (r, p)-capacities on P-m0 (M), r is an element of N, p > 1, which generalises a result due...
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作者：Kohatsu-Higa, A
作者单位：Pompeu Fabra University
摘要：In this article, we generalize the lower bound estimates for uniformly elliptic diffusion processes obtained by Kusuoka and Stroock. We define the concept of uniform elliptic random variable on Wiener space and show that with this definition one can prove a lower bound estimate of Gaussian type for its density. We apply our results to the case of the stochastic heat equation under the hypothesis of unifom ellipticity of the diffusion coefficient.
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作者：Del Moral, P; Ledoux, M; Miclo, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study Lipschitz contraction properties of general Markov kernels seen as operators on spaces of probability measures equipped with entropy-like distances''. Universal quantitative bounds on the associated ergodic constants are deduced from Dobrushin's ergodic coefficient. Strong contraction properties in Orlicz spaces for relative densities are proved under more restrictive mixing assumptions. We also describe contraction bounds in the entropy sense around arbitrary probability measures by ...
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作者：Virág, B
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Ito's excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint. The index is computed and equals 1/2.
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作者：Borovkov, AA
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：Let X-1, X-2, . . . be independent identically distributed random variables with regularly varying distribution tails: P(X-1 > t) = V(t) equivalent to t(-beta) L (t), P(X-1 < -t) = W(t) equivalent to t(-alpha) L-W(t), where alpha less than or equal to min(1, beta), and L and L-W are slowly varying functions as t --> infinity. Set S-n = X-1 + (. . .) + X-n, (S) over bar (n) = max(0less than or equal tokless than or equal ton) S-k. We find the asymptotic behavior of P(S-n > x) --> 0 and P(S (S) ...
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作者：Den Hollander, F; Nardi, FR; Olivieri, E; Scoppola, E
作者单位：University of Rome Tor Vergata; Roma Tre University; Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale per la Fisica della Materia (INFM-CNR)
摘要：The goal of this paper is to describe metastability and nucleation for a local version of the three-dimensional lattice gas with Kawasaki dynamics at low temperature and low density. Let Lambda subset of or equal to Z(3) be a large finite box. Particles perform simple exclusion on Lambda, but when they. occupy neighboring sites they feel a binding energy -U < 0 that slows down their dissociation. Along each bond touching the boundary of Lambda from the outside, particles are created with rate ...
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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...
