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作者：Dolera, Emanuele; Regazzini, Eugenio
作者单位：University of Pavia
摘要：In Dolera, Gabetta and Regazzini [Ann. Appl. Probab. 19 (2009) 186-201] it is proved that the total variation distance between the solution f(., t) of Kac's equation and the Gaussian density (0, sigma(2)) has an upper bound which goes to zero with an exponential rate equal to 1/4 as t -> +infinity. In the present paper, we determine a lower bound which decreases exponentially to zero with this same rate, provided that a suitable symmetrized form of f(0) has nonzero fourth cumulant kappa(4). Mo...
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作者：Doku-Amponsah, Kwabena; Moerters, Peter
作者单位：University of Ghana; University of Bath
摘要：For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed...
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作者：Dai, J. G.; He, Shuangchi; Tezcan, Tolga
作者单位：University System of Georgia; Georgia Institute of Technology; University of Illinois System; University of Illinois Urbana-Champaign; University of Rochester
摘要：This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded G/Ph/n + GI queues, where the patience times are independent and identically distributed following a general distribution. The next limit theorem is for overloaded G/Ph/n + M queues, where the patience time distribution is restricted to be exponential. We prove that a pair of diffusion-scaled ...
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作者：Alon, Noga; Gurel-Gurevich, Ori; Lubetzky, Eyal
作者单位：Tel Aviv University; Microsoft; MICROSOFT ISRAEL; Microsoft
摘要：In the classical balls-and-bins paradigm, where n balls are placed independently and uniformly in n bins, typically the number of bins with at least two balls in them is Theta(n) and the maximum number of balls in a bin is Theta(log n/log log n). It is well known that when each round offers k independent uniform options for bins, it is possible to typically achieve a constant maximal load if and only if k = Omega (log n). Moreover, it is possible w.h.p. to avoid any collisions between n/2 ball...
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作者：Azcue, Pablo; Muler, Nora
作者单位：Universidad Torcuato Di Tella
摘要：We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramer-Lundberg process. The firm has the option of investing part of the surplus in a Black-Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the...
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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 ...
