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作者：Marchal, P
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We define a class of processes on the boundary of a regular tree that can be viewed as stable Levy processes on (Z/n(0)Z)(N). We show that the range of these processes can be compared with a Bernoulli percolation as in Peres which easily leads to various results on the intersection properties. We develop an alternative approach based on the comparison with a branching random walk. By this method we establish the existence of points of infinite multiplicity when the index of the process equals ...
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作者：Möhle, M; Sagitov, S
作者单位：Johannes Gutenberg University of Mainz; Chalmers University of Technology; University of Gothenburg
摘要：We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as N --> infinity. It results in a full classification of the coalescent generators in the case of exchangeable reproduction. In general the coalescent process allows for simultaneous multiple mergers of ancestral lines.
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作者：Kenyon, R
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We define a scaling limit of the height function on the domino tiling model (dimer model) on simply connected regions in Z(2) and show that it is the massless free field, a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.
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作者：Davie, G
作者单位：University of South Africa
摘要：We formulate effective versions of the Borel-Cantelli lemmas using a coefficient from Kolmogorov complexity. We then use these effective versions to lift the effective content of the law of large numbers and the law of the iterated logarithm.
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作者：Krylov, NV
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The distributions of stochastic integrals are approximated by the distributions of stochastic integrals of piece-wise constant processes. The rate of approximation in some negative Sobolev spaces is estimated. Generalizations are given for problems arising in control theory.
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作者：Mason, DM; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let X-1,..., X-n, n greater than or equal to 1, be independent, identically distributed random variables and consider the Student t-statistic T-n based upon these random variables. Gine, Gotze and Mason (1997) proved that T-n converges in distribution to a standard normal random variable if and only if X is in the domain of attraction of a normal random variable and EX = 0. We shall show that roughly the same holds true for the bootstrapped Student t-statistic T-n*. In the process we shall dis...
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作者：Chassaing, P; Janson, S
作者单位：Universite de Lorraine; Uppsala University
摘要：We describe a Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed from a Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easily found. The three processes arise as limits, in three different ways, of profiles associated to ha...
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作者：Jonasson, J
作者单位：University of Gothenburg; Chalmers University of Technology
摘要：We consider a version of the Boolean (or Poisson blob) continuum percolation model where, at each point of a Poisson point process in the Euclidean plane with intensity lambda, a copy of a given compact convex set A with fixed rotation is placed. To each A we associate a critical value lambda (c)(A) which is the infimum of intensities lambda for which the occupied component contains an unbounded connected component. It is shown that min{lambda (c)(A) : A convex of area a} is attained if A is a...
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作者：Caputo, P; Deuschel, JD
作者单位：Technical University of Berlin
摘要：We continue our study of large deviations of the empirical measures of a massless Gaussian field on Z(d), whose covariance is given by the Green function of a long-range random walk. In this paper we extend techniques and results of Bolthausen and Deuschel to the nonlocal case of a random walk in the domain of attraction of the symmetric alpha -stable law, with alpha epsilon (0, 2 boolean AND d). In particular, we show that critical large deviations occur at the capacity scale Nd-alpha, With a...
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作者：Dynkin, EB
作者单位：Cornell University
摘要：Superprocesses (under the name continuous state branching processes) appeared, first, in a pioneering work of S. Watanabe [J. Math.. Kyoto Univ. 8 (1968) 141-167]. Deep results on paths of the super-Brownian motion were obtained by Dawson, Perkins, Le Gall and others. In earlier papers, a superprocess was interpreted as a Markov process X-t in the space of measures. This is not sufficient for a probabilistic approach to boundary value problems. A reacher model based on the concept of exit meas...
