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作者：Crepey, Stephane; Song, Shiqi
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：On a probability space (Omega, A, Q), we consider two filtrations F subset of G and a G stopping time theta such that the G predictable processes coincide with F predictable processes on (0,theta]. In this setup, it is well known that, for any F semimartingale X, the process X theta- (X stopped right before theta) is a G semimartingale. Given a positive constant T, we call theta an invariance time if there exists a probability measure P equivalent to Q on F-T such that, for any (F, P) local ma...
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作者：Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin
作者单位：Utah System of Higher Education; University of Utah; Pohang University of Science & Technology (POSTECH); Michigan State University
摘要：Let xi denote space-time white noise, and consider the following stochastic partial differential equations on R+ x R: (i) (u) over dot = 1/2 u '' + u xi, started identically at one; and (ii) (Z) over dot = 1/2 Z '' + xi, started identically at zero. It is well known that the solution to (i) is intermittent, whereas the solution to (ii) is not. And the two equations are known to be in different universality classes. We prove that the tall peaks of both systems are multifractals in a natural lar...
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作者：Brzeniak, Zdzislaw; Motyl, Elzbieta; Ondrejat, Martin
作者单位：University of York - UK; University of Lodz; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：Building upon a recent work by two of the authors and J. Seidler on bw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an invariant measure to stochastic 2-D Navier-Stokes (with multiplicative noise) equations in unbounded domains. This answers an open question left after the first author and Y. Li proved a corresponding result in the case of an additive noise.
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作者：Damron, Michael; Lam, Wai-Kit; Wang, Xuan
作者单位：University System of Georgia; Georgia Institute of Technology; Indiana University System; Indiana University Bloomington
摘要：We consider first passage percolation on Z(2) with i.i.d. weights, whose distribution function satisfies F(0) = p(c) = 1/2. This is sometimes known as the critical case because large clusters of zero-weight edges force passage times to grow at most logarithmically, giving zero time constant. Denote T (0, partial derivative B(n)) as the passage time from the origin to the boundary of the box [-n, n] x [-n, n]. We characterize the limit behavior of T (0, partial derivative B (n)) by conditions o...
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作者：Wang, Feng-Yu
作者单位：Tianjin University; Swansea University
摘要：By using the local dimension-free Harnack inequality established on incomplete Riemannian manifolds, integrability conditions on the coefficients are presented for SDEs to imply the nonexplosion of solutions as well as the existence, uniqueness and regularity estimates of invariant probability measures. These conditions include a class of drifts unbounded on compact domains such that the usual Lyapunov conditions cannot be verified. The main results are extended to second-order differential op...
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作者：Bollobas, Bela; Duminil-Copin, Hugo; Morris, Robert; Smith, Paul
作者单位：University of Cambridge; University of Memphis; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Tel Aviv University
摘要：The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobas, Smith and Uzzell, and the critical threshold for percolation was determined up to a constant factor for all such models by the authors of this paper. Here, we develop and refine the techniques introduced in that paper in order to determine a sharp threshold for the Duarte model. This resolves a question of Mountford from 1995, and is the first result of its type for a model with drift.
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作者：Hsu, Elton P.; Wang, Yu; Wang, Zhenan
作者单位：Northwestern University; University of Washington; University of Washington Seattle
摘要：Under general conditions, we devise a stochastic version of De Giorgi iteration scheme for semilinear stochastic parabolic partial differential equation of the form partial derivative(t)u = div(A del u) + f(t, x, u) + g(i)(t, x, u)<(w)over dot>(i)(t) with progressively measurable diffusion coefficients. We use the scheme to show that the solution of the equation is almost surely Holder continuous in both space and time variables.
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作者：Deligiannidis, George; Kosloff, Zemer
作者单位：University of Oxford; University of Warwick
摘要：We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Folner property almost surely.
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作者：Li, Xinyi
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider simple random walk on Z(d), d >= 3. Motivated by the work of A.-S. Sznitman and the author in [Probab. Theory Related Fields 161 (2015) 309-350] and [Electron. J. Probab. 19 (2014) 1-26], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the set of points visited by a simple random walk. We derive asymptotic lower bounds that bring into play random interlacements. Although open at the moment, some of the lower bounds we o...
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作者：Tikhomirov, Konstantin; Youssef, Pierre
作者单位：University of Alberta
摘要：We connect this question to a problem of estimating the probability that the image of certain random matrices does not intersect with a subset of the unit sphere Sn-1. In this way, the case of a discretized Brownian motion is related to Gordon's escape theorem dealing with standard Gaussian matrices. We show that for the random walk BMn(i), i is an element of N, the convex hull of the first C-n steps (for a sufficiently large universal constant C) contains the origin with probability close to ...
