-
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.
-
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.
-
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...
-
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...
-
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...
-
作者：Burdzy, K; Chen, ZQ
作者单位：University of Washington; University of Washington Seattle
摘要：We define a local time flow of skew Brownian motions, that is, a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the Ray-Knight theorem on local times. In our case, however, the local time process viewed as a function of the spatial variable is a pure jump Markov process ...
-
作者：Penrose, MD
作者单位：Durham University
摘要：Suppose X = (X-x)(xis an element ofZ)(d) is a white noise process, and H(B), defined for finite subsets B of Z(d), is determined in a stationary way by the restriction of X to B. Using a martingale approach, we prove a central limit theorem (CLT) for H as B becomes large, subject to H satisfying a stabilization condition (the effect of changing X-x at a single site needs to be local). This CLT is then applied to component counts for percolation and Boolean models, to the size of the big cluste...
-
作者：Seidenfeld, T; Schervish, MJ; Kadane, JB
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：Improper regular conditional distributions (red's) given a sigma-field A have the following anomalous property. For sets A is an element of A, Pr(A \ A) is not always equal to the indicator of A. Such a property makes the conditional probability puzzling as a representation of uncertainty. When red's exist and the sigma-field,A is countably generated, then almost surely the red is proper. We give sufficient conditions for an red to be improper in a maximal sense, and show that these conditions...
-
作者：Einmahl, U; Kuelbs, J
作者单位：Universite Libre de Bruxelles; University of Wisconsin System; University of Wisconsin Madison
摘要：We identify the possible cluster sets for a general law of the iterated logarithm in the Banach space setting, and show that all the possible limit sets arise as cluster sets for some random vector in an arbitrary separable Banach space. This extends previous results obtained in finite dimensional Euclidean spaces.
-
作者：Holroyd, AE; Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：We consider the following problem: given an i.i.d. family of Bernoulli random variables indexed by Z(d), find a random occupied site X is an element of Z(d) such that relative to X, the other random variables are still i.i.d. Bernoulli. Results of Thorisson imply that such an X exists for all d. Liggett proved that for d = 1, there exists an X with tails P(\X\ greater than or equal to t) of order ct(-1/2), but none with finite 1/2th moment. We prove that for general d there exists a solution w...
