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作者：Ferrari, PA; Pimentel, LPR
作者单位：Universidade de Sao Paulo
摘要：The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z(2). We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptot...
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作者：Barthe, F; Guédon, O; Mendelson, S; Naor, A
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Australian National University; Microsoft
摘要：This article investigates, by probabilistic methods, various geometric questions on B-p(n), the unit ball of l(p)(n). We propose realizations in terms of independent random variables of several distributions on B-p(n), including the P normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B-p(n), As another application, we compute moments of linear functionals on B-p(n) which gives sharp constants in Khinch...
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作者：Le Gall, JF; Mytnik, L
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Technion Israel Institute of Technology
摘要：This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1 + beta)-stable branching mechanism. It establishes the continuity of the density in dimension d = 2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutio...
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作者：Mikulevicius, R; Rozovskii, BL
作者单位：University of Southern California; University of Southern California
摘要：This paper concerns the Cauchy problem in R-d for the stochastic Navier-Stokes equation partial derivativetu = Deltau - (u, del)u - delp + f(u) + [(sigma, del)u - delp + g(u)] o W, u(0) = u(0), div u = 0, driven by white noise W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global stron...
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作者：Pitman, J; Winkel, M
作者单位：University of California System; University of California Berkeley; University of Oxford
摘要：Trees in Brownian excursions have been studied since the late 1980s. Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion. In this paper we study a forest-valued Markov process which describes the growth of the Brownian forest. The key result is a composition rule for binary Galton-Watson forests with i.i.d. exponential branch lengths. We give elementary proofs of this composition rule and explain how it is intimately linked with Williams' deco...
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作者：Bessaih, H; Gubinelli, M; Russo, F
作者单位：University of Wyoming; Universite Paris 13
摘要：We study an evolution problem in the space of continuous loops in a three-dimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Holder regular loops with index greater than 1/3. When the Holder regularity of the initial condition X is smaller or equal to 1/2, we require X to be a rough path in the sense of Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310, System Control and Rough...
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作者：Cator, E; Groeneboom, P
作者单位：Delft University of Technology
摘要：We show that, for a stationary version of Hammersley's process, with Poisson sources on the positive x-axis, and Poisson sinks on the positive y-axis, an isolated second-class particle, located at the origin at time zero, moves asymptotically, with probability 1, along the characteristic of a conservation equation for Hammersley's process. This allows us to show that Hammersley's process without sinks or sources, as defined by Aldous and Diaconis [Probab. Theory Related Fields 10 (1995) 199-21...
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作者：Cox, JT; Perkins, EA
作者单位：Syracuse University; University of British Columbia
摘要：We show that a sequence of stochastic spatial Lotka-Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.
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作者：Peligrad, M; Utev, S
作者单位：University System of Ohio; University of Cincinnati; University of Nottingham
摘要：We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe [Ann. Probab. 28 (2000) 713-724]. Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed.
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作者：Nualart, D; Peccati, G
作者单位：University of Barcelona; Sorbonne Universite
摘要：We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes.
