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作者：Pardoux, Etienne; Piatnitski, Andrey
作者单位：Aix-Marseille Universite; UiT The Arctic University of Tromso
摘要：In this paper we study the homogenization of a nonautonomous parabolic equation with a large random rapidly oscillating potential in the case of one-dimensional spatial variable. We show that if the potential is a statistically homogeneous rapidly oscillating function of both temporal and spatial variables, then, under proper mixing assumptions, the limit equation is deterministic, and convergence in probability holds. To the contrary, for the potential having a microstructure only in one of t...
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作者：Privault, Nicolas
作者单位：Nanyang Technological University
摘要：We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the central moments of Poisson stochastic integrals.
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作者：Roy, Emmanuel
作者单位：Universite Paris Cite
摘要：We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Levy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.
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作者：Dawson, Donald A.; Li, Zenghu
作者单位：Carleton University; Beijing Normal University
摘要：We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming-Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatment...
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作者：Chaumont, Loic; Kyprianou, Andreas; Carlos Pardo, Juan; Rivero, Victor
作者单位：Universite d'Angers; University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：For a positive self-similar Markov process, X, we construct a local time for the random set, Theta, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its past supremum. Next, we define and study the ladder process (R, H) associated to a positive self-similar Markov process X, namely a bivariate Markov process with a scaling property whose coordinates are the right inverse of the local time of the random set The...
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作者：Jin, Xiong
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.
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作者：Aaronson, Jon
作者单位：Tel Aviv University
摘要：Relative complexity measures the complexity of a probability preserving transformation relative to a factor being a sequence of random variables whose exponential growth rate is the relative entropy of the extension. We prove distributional limit theorems for the relative complexity of certain zero entropy extensions: RWRSs whose associated random walks satisfy the alpha-stable CLT (1 < alpha <= 2). The results give invariants for relative isomorphism of these.
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作者：Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulalia; Wu, Dongsheng; Xiao, Yimin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; Universite Paris 13; University of Alabama System; University of Alabama Huntsville; Michigan State University
摘要：We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in R-d has double points if and only if d < 4N. In particular, in the critical case where d = 4N, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning k-multiple points in the critical case k(d ...
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作者：Dette, Holger; Nagel, Jan
作者单位：Ruhr University Bochum; Technical University of Munich
摘要：In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vector...
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作者：Ledoux, M.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Universitaire de France
摘要：We analyze from the viewpoint of an abstract Markov operator recent results by Nualart and Peccati, and Nourdin and Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we are led to introduce a notion of chaos associated to a Markov operator through its iterated gradients and present conditions on the (pure) point spectrum for a sequence of chaos eigenfunctions to converge to a Gaussian distribution. Convergence to gamma distr...
