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作者：Diaconis, Persi; Saloff-Coste, Laurent
作者单位：Stanford University; Cornell University
摘要：This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions of spectral gap and mixing time. Y. Peres has observed that for many families of Markov chains, there is a cutoff if and only if the product of spectral gap and mixing time tends to infinity. We establish this for arbitrary birth and death chains in continuous time when the convergence is measured ...
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作者：Majewski, Kurt
作者单位：Siemens AG; Siemens Germany
摘要：We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from cumulative arrival and service time processes which are assumed to satisfy an appropriate sample path large deviation principle. We establish logarithmic asymptotics of large deviations for waiting time, idle time, queue length, departure and sojourn-time proces...
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作者：Ney, P. E.; Vidyashankar, Anand N.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Cornell University
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作者：Atar, Rami; Mandelbaum, Avi; Shaikhet, Gennady
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：A queueing model has J >= 2 heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of 1 >= 2 classes can be served at these stations at different rates, that depend on both the class and the station. A system administrator dynamically controls scheduling and routing. We study this model in the central limit theorem (or heavy traffic) regime proposed by Haffin and Whitt. We derive a diffusion model on R-I with a singular control term t...
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作者：Kramkov, Dmitry; Sirbu, Mihai
作者单位：Carnegie Mellon University; Columbia University
摘要：In the general framework of a semimartingale financial model and a utility function U defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a small number of random endowments. We show that this linear approximation has some important qualitative properties if and only if there is a risk-tolerance wealth process. In particular, they hold true in the following polar cases: 1. for any utility function U, if and only if the set of...
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作者：Saidi, Youssef; Zakoian, Jean-Michel
作者单位：Mohammed V University in Rabat; Institut Polytechnique de Paris; ENSAE Paris; Universite de Lille
摘要：A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and beta-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis.
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作者：Antunes, Nelson; Fricker, Christine; Robert, Philippe; Tibi, Danielle
作者单位：Universidade do Algarve; Universite Paris Cite
摘要：This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have reversibility properties, so the explicit expression of their invariant distribution is not known. Kelly's limiting regime is considered: the arrival rates of calls as well as the capacities of the nodes are proportional to a factor going to infinity. It is proved that,...
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作者：Dong, Rui; Goldschmidt, Christina; Martin, James B.
作者单位：University of California System; University of California Berkeley; University of Cambridge; University of Oxford
摘要：In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose sum is 1) and the two-parameter family of Poisson-Dirichlet distributions PD(alpha, theta) that take values in this space. We introduce families of random fragmentation and coagulation operators Frag(alpha) and Coag(alpha),(theta), respectively, with the following property: if the input to Frag(alp...
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作者：Li, Xun; Zhou, Xun Yu
作者单位：National University of Singapore; Chinese University of Hong Kong
摘要：This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient a la Markowitz. It is shown that, when the market coefficients are deterministic functions of time, a mean-variance efficient portfolio realizes the (discounted) targeted return on or before the terminal date with a probability greater than 0...
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作者：Piau, Didier
作者单位：Universite Claude Bernard Lyon 1; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population k is greater than a first threshold m(1) >= 1. If, furthermore, k is greater than a second threshold m(2) >= m(1), the normalized mean inverse population is at most 1/(k - m(2)). We express m(1) and m(2) as explicit functionals of the reproducing distribution, we discuss some analogues...
