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作者：Holst, L.; Quine, M. P.; Robinson, J.
作者单位：Royal Institute of Technology; University of Sydney
摘要：The model considered here has arisen in a number of completely separate contexts: release of neurotransmitter at neuromuscular synapses, unravelling of strands of DNA, differentiation of cells into heterocysts in algae and growth of crystals. After a shear transformation the model becomes a Markov process, based on a Poisson process on the upper half plane, homogeneous in the horizontal (time) direction, which increases at unit rate except for occasional drops. By considering the process separ...
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作者：Cohn, Harry
作者单位：University of Melbourne
摘要：Let {Zn} be a branching process whose offspring distributions vary with n. It is shown that the sequence {max(i > 0) P(Z(n) = i)} has a limit. Denote this limit by M. It turns out that M is positive only if the offspring variables rapidly approach constants. Let {c(n)} be a sequence of constants and Wn sZnrcn. It will be proven that M = 0 is necessary and sufficient for the limit distribution functions of all convergent {W-n} to be continuous on (0,infinity). If M > 0 there is, up to an equiva...
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作者：Gnedin, Alexander V.; Krengel, Ulrich
作者单位：University of Gottingen
摘要：We consider optimal stopping problems with loss function q depending on the rank of the stopped random variable. Samuels asked whether there exists an exchangeable sequence of random variables X-1,..., X-n without ties for which the observation of the values of the X-i's gives no advantage in comparison with the observation of just the relative ranks of the variables. We call distributions of the sequences with this property q-noninformative and derive necessary and sufficient conditions for t...
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作者：Yukich, J. E.
作者单位：Lehigh University
摘要：We show that the stochastic versions of some classical problems in combinatorial optimization may be imbedded in multiparameter subadditive processes having an intrinsic ergodic structure. A multiparameter generalization of Kingman's subadditive ergodic theorem is used to capture strong laws for these optimization problems, including the traveling salesman and minimal spanning tree processes. In this way we make progress on some open problems and provide alternate proofs of some well known asy...
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作者：Alsmeyer, Gerold; Roesler, Uwe
作者单位：University of Munster; University of Kiel
摘要：We consider the bisexual Galton-Watson process (BGWP) with promiscuous mating, that is, a branching process which behaves like an ordinary Galton-Watson process as long as at least one male is produced in each generation. For the case of Poissonian reproduction, it was pointed out by Daley, Hull and Taylor that the extinction probability of such a BGWP apparently behaves like a constant times the respective probability of its asexual counterpart (where males do not matter) providing the number...
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作者：Chen, Hong
作者单位：University of British Columbia
摘要：Dupuis and Williams proved that a sufficient condition for the positive recurrence and the existence of a unique stationary distribution for a semimartingale reflecting Brownian motion in an orthant (SRBM) is that all solutions of an associated deterministic Skorohod problem are attracted to the origin. In this paper, we derive a sufficient condition under which we can construct an explicit linear Lyapunov function for the Skorohod problem. Thus, this implies a sufficient condition for the sta...
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作者：Katehakis, Michael N.; Rothblum, Uriel G.
作者单位：Rutgers University System; Rutgers University Newark; Rutgers University New Brunswick; Technion Israel Institute of Technology
摘要：We express Gittins indices for multi-armed bandit problems as Laurent expansions around discount factor 1. The coefficients of these expansions are then used to characterize stationary optimal policies when the optimality criteria are sensitive-discount optimality (otherwise known as Blackwell optimality), average-reward optimality and average-overtaking optimality. We also obtain bounds and derive optimality conditions for policies of a type that continue playing the same bandit as long as th...
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作者：Dassios, Angelos
作者单位：University of London; London School Economics & Political Science
摘要：The purpose of this note is to obtain a representation of the distribution of the alpha-quantile of a process with stationary and independent increments as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for a Brownian motion. The proof is based on already known discrete time results.
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作者：Diaconis, P.; Saloff-Coste, L.
作者单位：Harvard University; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous time. Some aspects of the theory simplify considerably with finite state spaces and we are able to give a self-contained development. Examples of applications include the study of a Metropolis chain f...
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作者：Bladt, Mogens
作者单位：Universidad Nacional Autonoma de Mexico
摘要：In this paper we consider the asymptotic time average variance of the actual waiting time of the PH/PH/1 queue. To this end Poisson's equation plays a major role, since the solution to Poisson's equation is shown to be intimately connected with the desired variance. We derive explicit solutions to Poisson's equation using phase-type methodology, and present some numerical examples.
