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作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain reactions from uniform samples of the population after the reaction. First, we consider nonhomogeneous processes, which are more adapted to real reactions. Second, recalling that the first moment estimator is analytically known only in the infinite populati...
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作者：Andjel, ED; Guiol, H
作者单位：Aix-Marseille Universite; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble
摘要：We show that if mu is an invariant measure for the long range exclusion process putting no mass on the full configuration, L is the formal generator of that process and f is a cylinder function, then Lf is an element of L-1 (d mu) and integral Lf d mu = 0. This result is then applied to determine (i) the set of invariant and translation-invariant measures of the long range exclusion process on Z(d) when the underlying random walk is irreducible; (ii) the set of invariant measures of the long r...
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作者：Samorodnitsky, G
作者单位：Cornell University
摘要：This paper elucidates the connection between stationary symmetric alpha-stable processes with 0 < alpha < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.
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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...
