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作者：Aghajani, Reza; Ramanan, Kavita
作者单位：University of California System; University of California San Diego; Brown University
摘要：We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by N identical servers in a first-come-first-serve manner. We introduce a two-component infinite-dimensional Markov process that serves as a diffusion model for this network, in the regime where the number of servers goes to infinity and the load on the network scales as 1 - beta N-1/2 + o(N-1/2) f...
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作者：Banerjee, Sayan; Mukherjee, Debankur
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：Consider a system of N parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate A(N). When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (Math. Oper. Res. 43 (2018) 867-886) established that in the Halfin-Whitt regime where (N - lambda(N))/root N -> beta > 0 as N -> infinity, appropriately scaled occupancy...
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作者：Bank, Peter; Dolinsky, Yan
作者单位：Technical University of Berlin; Hebrew University of Jerusalem; Monash University
摘要：We study super-replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable continuous time financial market models the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies. Our second result derives nontrivial scaling limits of super-replication prices for binomial models with small fixed cos...
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作者：Lachieze-Rey, Raphael; Schulte, Matthias; Yukich, J. E.
作者单位：Universite Paris Cite; University of Bern; Lehigh University
摘要：We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point processes on general metric spaces. The rates are valid whenever the geometric functional is expressible as a sum of exponentially stabilizing score functions satisfying a moment condition. By incorporating stabilization methods into the Malliavin-Stein theory, we obtain rates of normal approximation for sums of stab...
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作者：Figueroa-Lopez, Jose E.; Olafsson, Sveinn
作者单位：Washington University (WUSTL); University of California System; University of California Santa Barbara
摘要：Since the work of Page in the 1950s, the problem of detecting an abrupt change in the distribution of stochastic processes has received a great deal of attention. In particular, a deep connection has been established between Lorden's minimax approach to change-point detection and the widely used CUSUM procedure, first for discrete-time processes, and subsequently for some of their continuous-time counterparts. However, results for processes with jumps are still scarce, while the practical impo...
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作者：Liu, Yanghui; Tindel, Samy
作者单位：Purdue University System; Purdue University
摘要：In this article, we consider the so-called modified Euler scheme for stochastic differential equations (SDEs) driven by fractional Brownian motions (fBm) with Hurst parameter 1/3 < H < 1/2. This is a first-order time-discrete numerical approximation scheme, and has been introduced in [Ann. Appl. Probab. 26 (2016) 1147-1207] recently in order to generalize the classical Euler scheme for Ito SDEs to the case H > 1/2. The current contribution generalizes the modified Euler scheme to the rough cas...
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作者：Cruise, James R.; Wade, Andrew R.
作者单位：Heriot Watt University; Durham University
摘要：Each site of Z hosts a queue with arrival rate lambda. A single server, starting at the origin, serves its current queue at rate mu until that queue is empty, and then moves to the longest neighbouring queue. In the critical case lambda = mu, we show that the server returns to every site infinitely often. We also give a sharp iterated logarithm result for the server's position. Important ingredients in the proofs are that the times between successive queues being emptied exhibit doubly exponen...
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作者：Bishop, A. N.; Del Moral, P.; Kamatani, K.; Remillard, B.
作者单位：University of Technology Sydney; Commonwealth Scientific & Industrial Research Organisation (CSIRO); Inria; Centre National de la Recherche Scientifique (CNRS); University of New South Wales Sydney; University of Osaka; Universite de Montreal; HEC Montreal
摘要：This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a non-Lipschitz continuous diffusion function. We present a novel approach, combining tangent process techniques, Feynman-Kac path integration and exponential change of measures, to derive sharp exponential decays to equilibrium. We also provide uniform estimates with...
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作者：Barbour, A. D.; Rollin, Adrian
作者单位：University of Zurich; National University of Singapore
摘要：We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form T := Sigma(v is an element of V) H-v, where V is the vertex set, and H-v depends on a neighbourhood in the graph around v of size at most l. The error bound is expressed in terms of l, vertical bar V vertical bar, an almost sure bound on H-v, the maximum vert...
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作者：Arapostathis, Ari; Pang, Guodong; Sandric, Nikola
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Zagreb
摘要：We study the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or asymptotically negligible service interruptions in the Halfin-Whitt regime as special cases. In these queueing models, the Ito equations have a piecewise linear drift, and are driven by either (1) a Brownian motion and a pure-jump Levy process, or (2) an ani...
