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作者：Benois, O.
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a large deviation principle for the density field of independent particle systems in an infinite volume. We then deduce from the one-dimensional case of this result the large deviations for the occupation times of various sets (from microscopic to macroscopic scales) and we recover the theorem established by Cox and Griffeath. An expression of the rate function is given using the Brownian motion local time as in Deuschel and Wang.
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作者：Pacheco, Antonio; Prabhu, N. U.
作者单位：Universidade de Lisboa; Cornell University
摘要：We investigate a storage model where the input and the demand are additive functionals on a Markov chain J. The storage policy is to meet the largest possible portion of the demand. We first derive results for the net input process embedded at the epochs of transitions of J, which is a Markov random walk. Our analysis is based on a Wiener-Hopf factorization for this random walk; this also gives results for the busy period of the storage process. The properties of the storage level and the unsa...
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作者：Malyshev, Vadim A.; Yakovlev, Andrei V.
作者单位：Inria; Universite de Orleans
摘要：We consider finite closed Jackson networks with N first come, first serve nodes and M customers. In the limit M ->infinity, N -> infinity, M/N -> lambda > 0, we get conditions when mean queue lengths are uniformly bounded and when there exists a node where the mean queue length tends to infinity under the above limit (condensation phenomena, traffic jams), in terms of the limit distribution of the relative utilizations of the nodes. In the same terms, we also derive asymptotics of the partitio...
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作者：Hwang, Hsien-Kuei
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Academia Sinica - Taiwan
摘要：We prove a general central limit theorem for probabilities of large deviations for sequences of random variables satisfying certain analytic conditions. This theorem has wide applications to combinatorial structures and to the distribution of additive arithmetical functions. The method of proof is an extension of Kubilius' version of Cramer's classical method based on analytic moment generating functions. We thus generalize Cramer's and Kubilius's theorems on large deviations.
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作者：Lund, Robert B.; Meyn, Sean P.; Tweedie, Richard L.
作者单位：University System of Georgia; University of Georgia; University of Illinois System; University of Illinois Urbana-Champaign; Colorado State University System; Colorado State University Fort Collins
摘要：Let {Phi(t), t >= 0} be a Markov process on the state space [0, infinity) that is stochastically ordered in its initial state. Examples of such processes include server workloads in queues, birth-and-death processes, storage and insurance risk processes and reflected diffusions. We consider the existence of a limiting probability measure pi or and an exponential convergence rate alpha > 0 such that lim (t -> infinity) e(alpha t)sup(Lambda)vertical bar P-x [Phi(t) is an element of A] - pi(A)ver...
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作者：Hajek, Bruce
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：A set of nodes and a set of consumers are given, and to each consumer there corresponds a subset of the nodes. Each consumer has a demand, which is a load to be distributed among the nodes corresponding to the consumer. The load at a node is the sum of the loads placed on the node by all consumers. The load is balanced if no single consumer can shift some load from one node to another to reduce the absolute difference between the total loads at the two nodes. The model provides a setting to st...
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作者：Baccelli, Francois; Schmidt, Volker
作者单位：Ulm University
摘要：We give a Taylor series expansion for the mean value of the canonical stationary state variables of open (max, +)-linear stochastic systems with Poisson input process. Probabilistic expressions are derived for coefficients of all orders, under certain integrability conditions. The coefficients in the series expansion are the expectations of polynomials, known in explicit form, of certain random variables defined from the data of the (max, +)linear system. These polynomials are of independent c...
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作者：Harrison, J. M.; Williams, J.
作者单位：Stanford University; University of California System; University of California San Diego
摘要：We consider a multiclass closed queueing network model analogous to the open network models of Rybko and Stolyar and of Lu and Kumar. The closed network has two single-server stations and a fixed customer population of size n. Customers are routed in cyclic fashion through four distinct classes, two of which are served at each station, and each server uses a preemptive-resume priority discipline. The service time distribution for each customer class is exponential, and attention is focused on ...
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作者：Burdzy, Krzysztof; Madrecki, Andrzej
作者单位：University of Washington; University of Washington Seattle; Wroclaw University of Science & Technology
摘要：We study an asymptotically 4-stable process. The main result is an Ito type formula.
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作者：Kella, Offer
作者单位：Hebrew University of Jerusalem
摘要：We consider a stochastic fluid network with inputs which are independent subordinators. We show that under some natural conditions the distribution of the fluid content process converges in total variation to a proper limit and that the limiting distribution has a positive mass at the origin. As a consequence of the methodology used, we obtain upper and lower bounds for the expected values of this limiting distribution. For the two-dimensional case, under certain conditions, explicit formulas ...
