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作者：Ata, Baris; Gurvich, Itai
作者单位：Northwestern University
摘要：We consider optimal control of a multi-class queue in the Halfin-Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide asymptotically optimal controls with optimality gaps of o(root n) where n is the system size, for example, the number of servers. We construct a sequence of asymptotically optimal controls where the optimality gap grows logarithmically with the system size. Our analysis ...
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作者：Jeanblanc, Monique; Mania, Michael; Santacroce, Marina; Schweizer, Martin
作者单位：Universite Paris Saclay; Polytechnic University of Turin; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI)
摘要：We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterize its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional mean-variance hedging problem. For comparison with the existing...
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作者：Nagai, Hideo
作者单位：University of Osaka
摘要：We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model, and then study the asymptotic behavior of minimizing probability as T -> infinity. This problem can be closely related to an ergodic risk-sensitive stochastic control problem in the risk-averse case. Indeed, in our main theorem, we relate the former problem concerning the asymptotics for risk minimization to the latter as its dual. As a result...
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作者：Shah, Devavrat; Wischik, Damon
作者单位：Massachusetts Institute of Technology (MIT); University of London; University College London
摘要：We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time. We consider a family of scheduling policies, related to the maximum-weight policy of Tassiulas and Ephremides [IEEE Trans. Automat. Control 37 (1992) 1936-1948], for single-hop and multihop networks. We specify a fl...
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作者：de Bouard, A.; Gazeau, M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrodinger equations. This system arises ill the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Gamier and Marty [Wave Motion 43 (2006) 544-560], Marty [Problemes d'evolution en milieux aleatoires: Theoremes limites, schemas...
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作者：Garet, Olivier; Marchand, Regine
作者单位：Universite de Lorraine
摘要：The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H-t denotes the set of already occupied sites at time t, we show that for almost every environment, when the contact process survives, the set H-t/t almost surely converges to a compact set that only depends on the law of the environment. To this aim, we prove a new almost subadditive...
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作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：In this article we study a class of stochastic functional differential equations driven by Levy processes (in particular, alpha-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals. This corresponds to the local solvability to a class of quasi-linear partial integro-differential equations. Moreover, in the constant diffusion coefficient case, without any assumptions on the Levy generator, we also show the existence of a unique maximal weak solu...
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作者：Broutin, Nicolas; Holmgren, Cecilia
作者单位：University of Cambridge
摘要：We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion in the nodes of a tree. The total path length (sum of depths of the items) is a natural measure of the efficiency of the algorithm/data structure. Using renewal theory, we prove convergence in distribution of the total path length toward a distribution charac...
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作者：Benjamin, Itai; Makarychev, Yury
作者单位：Weizmann Institute of Science; Toyota Technological Institute - Chicago
摘要：Suppose we sequentially put n balls into n bins. If we put each ball into a random bin then the heaviest bin will contain similar to log n/log log n balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180-200] showed that if each time we choose two bins at random and put the ball in the least loaded bin among the two, then the heaviest bin will contain only similar to log log n balls with high probability. How much memory do we need to implement this...
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作者：Wood, Philip Matchett
作者单位：Stanford University
摘要：The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the eigenvalues of a random sign matrix, where each entry is +1 or -1 with equal probability, looks the same as an analogous plot of the eigenvalues of a random matrix where each entry is complex Gaussian with zero mean and unit variance. In the current paper, we prove...
