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作者：Mohamed, Hanene; Robert, Philippe
作者单位：Universite Paris Saclay; Inria
摘要：In this paper, a general tree algorithm processing a random flow of arrivals is analyzed. Capetanakis-Tsybakov-Mikhailov's protocol in the context of communication networks with random access is an example of such an algorithm. In computer science, this corresponds to a trie structure with a dynamic input. Mathematically, it is related to a stopped branching process with exogeneous arrivals (immigration). Under quite general assumptions on the distribution of the number of arrivals and on the ...
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作者：Bordenave, Charles; Torrisi, Giovanni Luca
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Rome Tor Vergata; Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
摘要：We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and n objects spatially uniformly distributed, each object being allocated to a bin at a cost depending on its position. Two allocations are considered: the allocation minimizing the bin loads and the allocation allocating each object to its less costly bin. We analyze the asymptotic properties of these allocations as the number of objects grows to infinity...
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作者：Krieger, Abba M.; Pollak, Moshe; Samuel-Cahn, Ester
作者单位：University of Pennsylvania; Hebrew University of Jerusalem
摘要：The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distributions. This class contains the Normal, Lognormal, Gamma, Weibull and many other distributions. The selection rules are the better than average (beta = 1) and the beta-better than average rule, defined as follows. After the first item is selected, another item is...
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作者：Kargin, Vladislav
作者单位：Stanford University
摘要：Suppose that X(1), ... , X(n), ... are i.i.d. rotationally invariant N-by-N matrices. Let Pi(n) = X(n) ... X(1). It is known that n(-1) log vertical bar Pi(n)vertical bar converges to a non-random limit. We prove that under certain additional assumptions on matrices X(i) the speed of convergence to this limit does not decrease when the size of matrices, N, grows.
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作者：Barrera, Javiera; Fontbona, Joaquin
作者单位：Universidad Adolfo Ibanez; Universidad de Chile; Universidad de Chile
摘要：We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a law of large numbers for random partitions, a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split a...
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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...
