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作者：Peterson, Jonathon; Zeitouni, Ofer
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：We consider it nearest-neighbor, one dimensional random walk (X-n)(n >= 0) in a random i.i.d. environment. in the regime where the walk is transient but with zero speed, so that X-n is of order n(s) for some s < 1. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: There exist sequences {n(k)} and {x(k)} depending on the environment only, such that Xn(k) - x(k) = 0(logn(k))(2) (a localized regime). On the other hand, there exist sequences {t...
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作者：Rasonyi, Miklos; Schachermayer, Walter; Warnung, Richard
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control; University of Vienna
摘要：In this article we consider a Brownian motion with drift of the form dS(t) = mu(t)dt + dB(t) for t >= 0, with a specific nontrivial (mu(t))(t) >= 0, predictable with respect to F-B, the natural filtration of the Brownian motion B = (B-t)(t >= 0). We construct a process H = (H-t)(t >= 0), also predictable with respect to F-B such that ((H center dot S)(t))(t >= 0) is a Brownian motion in its own filtration. Furthermore, for any delta > 0, we refine this construction such that the drift (mu(t))(...
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作者：Cattiaux, Patrick; Collet, Pierre; Lambert, Amaury; Martinez, Servet; Meleard, Sylvie; San Martin, Jaime
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Sorbonne Universite; Universite Paris Cite; Universidad de Chile; Universidad de Chile
摘要：In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to -infinity at the origin, and the diffusion to have an entrance boundary at +infinity. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth-death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with pr...
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作者：Barbu, Viorel; Da Prat, Giuseppe; Tubaro, Luciano
作者单位：Alexandru Ioan Cuza University; Scuola Normale Superiore di Pisa; University of Trento
摘要：We consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set K with nonempty interior and regular boundary Sigma in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on Sigma.
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作者：Doob, J. L.
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作者：Bressaud, Xavier; Fournier, Nicolas
作者单位：Aix-Marseille Universite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We consider an interacting particle system (eta(t))t >= 0 with values in {0, 1}(Z), in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to its size. We show that such a process admits a unique invariant distribution, which is exponentially mixing and can be perfectly simulated. We also prove that for any initial condition, the avalanche process tends to equilibrium exponentially fast, as time increases to infini...
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作者：Lowther, George
摘要：In this paper, we took at the properties of limits of a sequence of real valued inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions, then the limit does not have to be a diffusion. However, we show that as long as the drift terms satisfy a Lipschitz condition and the limit is continuous in probability, then it will lie in a class of processes that we refer to as the almost-continuous diffusions. These processes are strong Markov and satisfy an al...
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作者：Imkeller, Peter; Pavlyukevich, Ilya; Wetzel, Torsten
作者单位：Humboldt University of Berlin
摘要：We consider a dynamical system described by the differential equation (Y) over dot(t) = -U'(Y-t) with a unique stable point at the origin. We perturb the system by the Levy noise of intensity E to obtain the stochastic differential equation dX(t)(epsilon) = -U'(X-t-(epsilon)) dt + epsilon dL(t). The process L is a symmetric Levy process whose jump measure nu has exponentially light tails, nu([u, infinity)) similar to exp(- u(alpha)), alpha > 0, u -> infinity. We study the first exit problem fo...
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作者：Melbourne, Ian; Nicol, Matthew
作者单位：University of Surrey; University of Houston System; University of Houston
摘要：We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modeled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.
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作者：Capitaine, Mireille; Donati-Martin, Catherine; Feral, Delphine
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
摘要：In this paper, we investigate the asymptotic spectrum of complex or real Deformed Wigner matrices (M-N)(N) defined by M-N = W-N/root N + A(N) where W-N is all N x N Hermitian (resp., symmetric) Wigner matrix whose entries have a symmetric law satisfying a Poincare inequality. The matrix A(N) is Hermitian (resp., symmetric) and deterministic with all but finitely many eigenvalues equal to zero. We first show that, as soon as the first largest or last smallest eigenvalues of A(N) are sufficientl...
