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作者：Evans, Steven N.; Ralph, Peter L.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Davis
摘要：If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting MRCA age process has been studied previously when the population has a constant large size and evolves via the diffusion limit of standard Wright-Fisher dynamics. For any population model, the sample paths of the MRCA age process are made up of periods of linear upward d...
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作者：Hata, Hiroaki; Nagai, Hideo; Sheu, Shuenn-Jyi
作者单位：Academia Sinica - Taiwan; University of Osaka
摘要：We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently large time horizon. Indeed, in our theorem we state a duality in the relation between the above two problems. Furthermore, under a multidimensional linear Gaussian model we obtain...
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作者：Puhalskii, Anatolii A.; Reed, Josh E.
作者单位：University of Colorado System; University of Colorado Denver; New York University
摘要：We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit process does not have trajectories in the Skorohal space. We give conditions for the convergence to hold in the topology of compact convergence. Some new results for an infinite server are also provided.
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作者：James, Lancelot F.
作者单位：Hong Kong University of Science & Technology
摘要：This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an alpha-stable law, for 0 < alpha < 1, and the other variable has the law defined by polynomially tilting the density of an alpha-stable random variable by a factor theta > -alpha. When theta = 0, these variables equate with the ratio investigated by Lamperti [Trans. Amer. Math. Soc. 88 (1958) 380-387] which, remarkably, was shown to h...
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作者：Baumdicker, F.; Hess, W. R.; Pfaffelhuber, P.
作者单位：University of Freiburg; University of Freiburg
摘要：The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to generation. We use the random genealogy given by a Kingman coalescent in order to superimpose events of gene gain and loss along ancestral lines. Gene gains occur at a constant rate along ancestral lines. We assume that gained genes have never been present in the ...
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作者：Saloff-Coste, L.; Zuniga, J.
作者单位：Cornell University; Stanford University
摘要：Starting from a given Markov kernel on a finite set V and a bijection g of V, we construct and study a time inhomogeneous Markov chain whose kernel at time n is obtained from K by transport of g(n-1). We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.
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作者：Lemaire, Vincent; Pages, Gilles
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：We propose an unconstrained stochastic approximation method for finding the optimal change of measure (in an a priori parametric family) to reduce the variance of a Monte Carlo simulation. We consider different parametric families based on the Girsanov theorem and the Esscher transform (exponential-tilting). In [Monte Carlo Methods Appl. 10 (2004) 1-24], it described a projected Robbins-Monro procedure to select the parameter minimizing the variance in a multidimensional Gaussian framework. In...
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作者：Haas, Benedicte
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：The subject of this paper is a fragmentation equation with nonconservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the fragmentation rate, we describe the large time behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equation are constructed via nonincreasing self-similar Markov processes that continuously reach 0 in finite tim...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore County; Brown University
摘要：This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if the time before possible entry into service exceeds the patience time. The dynamics of the system is represented in terms of a pair of measure-valued processes, one that keeps track of the waiting times of the customers in queue and the other that keeps trac...
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作者：Bhamidi, Shankar; van der Hofstad, Remco; Hooghiemstra, Gerard
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology; Delft University of Technology
摘要：We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly chosen connected vertices in the network, as well as for the number of edges on the least weight path, the so-called hopcount. We analyze the configuration model with degree power-law exponentt tau > 2, in which the degrees are assumed to be i.i.d. with a tail di...
