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作者：DONNELLY, P; JOYCE, P
作者单位：University of Idaho; University of Southern California
摘要：The population genealogical processes associated with a wide range of exchangeable reproductive models (including the Wright-Fisher model) are shown to converge weakly, as the population size becomes large, to a particularly tractable limiting process, the age-ordered analog of Kingman's coalescent. This result extends the known convergence results for sample processes and effectively completes the robustness theory for neutral genealogies. Its consequences, which include a unification of the ...
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作者：SCHONMANN, RH
作者单位：Universidade de Sao Paulo
摘要：We consider some deterministic cellular automata on the state space {0, 1}L(d) evolving in discrete time, starting from product measures. Basic features of the dynamics include: 1's do not change, translation invariance, attractiveness and nearest neighbor interaction. The class of models which is studied generalizes the bootstrap percolation rules, in which a 0 changes to a 1 when it has at least l neighbors which are 1. Our main concern is with critical phenomena occurring with these models....
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作者：TRIBE, R
摘要：In this paper we use a martingale problem characterization to study the behavior of finite measure valued superprocesses with a variety of spatial motions. In general the superprocess, when normalized to be a probability, will converge to a point mass at its extinction time. For some spatial motions we prove that there are times near extinction at which the closed support of the process is concentrated near one point. We obtain a Tanaka formula for the measure of a half space under a one dimen...
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作者：BACCELLI, F; LIU, Z
摘要：This paper is concerned with a class of stochastic recursive sequences that arise in various branches of queueing theory. First, we make use of Kingman's subadditive ergodic theorem to determine the stability region of this type of sequence, or equivalently, the condition under which they converge weakly to a finite limit. Under this stability condition, we also show that these sequences admit a unique finite stationary regime and that regardless of the initial condition, the transient sequenc...
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作者：ZABELL, SL
摘要：A probability measure on the sphere is absolutely continuous with respect to the uniform measure on the sphere if and only if the probability of any open set varies continuously as the sphere is rotated. In general, if a topological group G acts transitively on a topological space S, and both are Hausdorff, locally compact and second countable, then a probability measure v on the Borel sets of S is absolutely continuous with respect to the unique invariant measure class on S if and only if the...
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作者：BERMAN, SM
摘要：Let X(t) be a stationary vector Gaussian process in R(m) whose components are independent copies of a real stationary Gaussian process with covariance function r(t). Let phi(z) be the standard normal density and, for t > 0, epsilon > 0, consider the double integral [GRAPHICS] which represents an approximate self-intersection local time of X(s), 0 less-than-or-equal-to s less-than-or-equal-to t. Under the sole condition r is-an-element-of L2, the double integral has, upon suitable normalization...
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作者：KALIKOW, S; WEISS, B
作者单位：Hebrew University of Jerusalem
摘要：Some explicit isomorphisms are constructed between Bernoulli shifts with infinite entropy.
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作者：AVRAM, F; TAQQU, MS
作者单位：Boston University; University of North Carolina; University of North Carolina Chapel Hill
摘要：Skorohod has shown that the convergence of sums of i.i.d. random variables to an alpha-stable Levy motion, with 0 < alpha < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving averages with at least two nonzero coefficients, weak-J1 convergence cannot hold because adjacent jumps of the process can coalesce in the limit; however, if the moving average coefficients are positive, then the adjacent jumps are essentially monotone and one can hav...
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作者：BACCELLI, F
摘要：Stochastic Petri networks provide a general formalism for describing the dynamics of discrete event systems. The present paper focuses on a subclass of stochastic Petri networks called stochastic event graphs, under the assumption that the variables used for their timing form stationary and ergodic sequences of random variables. We show that such stochastic event graphs can be seen as a (max, +) linear system in a random, stationary and ergodic environment. We then analyze the associated Lyapo...
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作者：SHIELDS, PC
作者单位：Eotvos Lorand University
摘要：Grassberger suggested an interesting entropy estimator, namely, n log n/SIGMA(i = 1)nL(i)n, where L(i)n is the shortest prefix of x(i), x(i + 1),..., which is not a prefix of any other x(j), x(j + 1), for j less-than-or-equal-to n. We show that this estimator is not consistent for the general ergodic process, although it is consistent for Markov chains. A weaker trimmed mean type result is proved for the general case, namely, given epsilon > 0, eventually almost surely all but an epsilon-fract...
