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作者：Feng, Shui
作者单位：McMaster University
摘要：Several results of large deviations are obtained for distributions that are associated with the Poisson-Dirichlet distribution and the Ewens sampling formula when the parameter theta approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of theta going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of theta going to infinity in a Poisson-Dirichlet distribution corresponds to a finite ...
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作者：Bertacchi, Daniela; Posta, Gustavo; Zucca, Fabio
作者单位：University of Milan; Polytechnic University of Milan
摘要：We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a nontrivial invariant measure for this case.
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作者：Merlet, Glenn
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Let (A(n))(n is an element of N) be a stationary sequence of topical (i.e., isotone and additively homogeneous) operators. Let x (n, x(0)) be defined by x (0, x(0)) = x(0) and x (n + 1, x(0)) = A(n)x (n, x(0)). It can model a wide range of systems including train or queuing networks, job-shop, timed digital circuits or parallel processing systems. When (A(n))(n is an element of N) has the memory loss property, (x (n, x(0)))(n is an element of N) satisfies a strong law of large numbers. We show...
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作者：Jones, Matthew O.; Serfozo, Richard F.
作者单位：Austin Peay State University; University System of Georgia; Georgia Institute of Technology
摘要：We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172-182] for sums of uniformly null point processes that have Poisson limits. Included is an application in which a particle-survivor point process converges to a Poisson process. This result sheds light on the surprising Poisson limit of the species competition process of Durrett and Limic.
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作者：Birkner, Matthias; Depperschmidt, Andrei
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：We study a discrete time spatial branching system on Z(d) With log iStic- type local regulation at each deme depending on a weighted average of the population in neighboring demes. We show that the system survives for all time with positive probability if the competition term is small enough. For a restricted set of parameter values, we also obtain uniqueness of the nontrivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model. Along the way we c...
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作者：Bai, Z. D.; Silverstein, Jack W.
作者单位：Northeast Normal University - China; North Carolina State University
摘要：Let {s(ij): i, j = 1,2....} consist of i.i.d. random variables in C with Es-11 = 0, E/s(11)/(2) = 1. For each positive integer N, let s(k) = s(k) (N) = (s(1k), s(2k),..., s(Nk))(T), 1 <= k <= K, with K = K(N) and K/N -> c > 0 as N -> infinity. Assume for fixed positive integer L, for each N and k <= K, alpha(k) = (alpha(k)(1),..., alpha k(L))(T) is random, independent of the s(ij), and the empirical distribution of (alpha(1),..., alpha(K)), with probability one converging weakly to a probabili...
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作者：Yin, George; Zhang, Hanqin
作者单位：Wayne State University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale scenarios naturally arise. One of the important questions is: As the rate of fluctuation of the Markov chain goes to infinity, if the limit distributions of suitably centered and scaled sequences of occupation measures exist, what can be said about the converg...
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作者：Gouere, Jean-Baptiste
作者单位：Universite de Orleans
摘要：We study two competing growth models. Each of these models describes the spread of a finite number of infections on a graph. Each infection evolves like an (oriented or unoriented) first passage percolation process except that once a vertex is infected by type i infection, it remains of type i forever. We give results about the shape of the area ultimately infected by the different infections.
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作者：Kochman, Fred; Reeds, Jim
作者单位：Center for Communications & Computing
摘要：According to a 1975 result of T. Kaijser, if some nonvanishing product of hidden Markov model (HMM) stepping matrices is subrectangular, and the underlying chain is aperiodic, the corresponding alpha-chain has a unique invariant limiting measure gimel. Here the alpha-chain {alpha(n)} = {(alpha(ni))} is given by alpha(ni) = P(X-n = i vertical bar Y-n, Yn-1, ...), where {(X-n, Y-n)} is a finite state HMM with unobserved Markov chain component {X-n} and observed output component {Y-n}. This defin...
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作者：Budhiraja, Amarjit; Ghosh, Arka Prasanna
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
摘要：We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural nonanticipativity condition for admissibility of control policies is introduced. The condition is seen to hold for a broad class of problems. Using this formulation of admissible controls and a time-transformation technique, we establish that the infimum of the cost for ...
