-
作者：Fricker, Christine; Robert, Philippe; Saada, Ellen; Tibi, Danielle
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie; Universite Paris Cite
摘要：In this paper we study a stochastic network model introduced recently in the analysis of neural networks. In this model the interaction between the nodes of the network is local: with each node is associated some real number (the inhibition in the language of neural networks) which is decreasing linearly with time. When this number reaches 0, it sends out some random input to its neighbors (a spike) and restarts with some random value. The state of our network is described as a Markov process....
-
作者：Chang, Joseph T.
作者单位：Yale University
摘要：Let X-1, X-2, ... be independent and identically distributed positive random variables with S-n = X-1 + ... +X-n, and for nonnegative b define R-b = inf{S-n - b: S-n > b}. Then R-b is called the overshoot at b. In terms of the moments of X-1, Lorden gave bounds for the moments of R-b that hold uniformly over all b. Using a coupling argument, we establish stochastic ordering inequalities that imply the moment inequalities of Lorden. In addition to simple new proofs of Lorden's inequalities, we ...
-
作者：Ferrari, P. A.; Fontes, L. R. G.
作者单位：Universidade de Sao Paulo
摘要：We study a system of infinitely many queues with Poisson arrivals and exponential service times. Let the net output process be the difference between the departure process and the arrival process. We impose certain ergodicity conditions on the underlying Markov chain governing the customer path. These conditions imply the existence of an invariant measure under which the average net output process is positive and proportional to the time. Starting the system with that measure, we prove that th...
-
作者：Malyshev, Vadim; Robert, Philippe
作者单位：Lomonosov Moscow State University; Inria
摘要：In this paper we analyze the following loss network: When a customer arrives at a node of the network, it is served by this node if the node is not occupied; otherwise it is transmitted to some empty node where it will be served at a different rate. For the simplest systems of this type with a very large number of nodes and with global sharing, we show the existence of second order phase transitions and present explicit formulas for probability characteristics. For local sharing, we study the ...
-
作者：Deuschel, Jean-Dominique; Mazza, Christian
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Fribourg
摘要：We study the convergence of nonsymmetric annealing processes, extending the classical Dirichlet form approach to a broad class of Markov chains with exponentially vanishing transition functions. We show that both the true and symmetrized spectral gaps are logarithmically equivalent, and give robust estimates for the gap using geometric methods.
-
作者：Massey, William A.; Whitt, Ward
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs
摘要：A fundamental problem that led to the development of queueing theory is the probabilistic modelling of the number of busy lines in telephone trunk groups. Based on the behavior of real telephone systems, a natural model to use would be the M-t/G/s/0 queue, which has s servers, no extra waiting space and a nonhomogeneous Poisson arrival process (M-t). Unfortunately, so far queueing theory has provided an exact analysis for only the M/G/s/0 queue in steady state, which yields the Erlang blocking...
-
作者：Quine, M. P.; Szczotka, W.
作者单位：University of Sydney
摘要：We define a stochastic process H = (X-n = 0, 1, 2, ...) in terms of cumulative sums of the sequence K-1, K-2, ... of integer-valued random variables in such a way that if the K-i, are independent, identically distributed and nonnegative, then H is a Bienayme Galton Watson branching process. By exploiting the fact that H is in a sense embedded in a random walk, we show that some standard branching process results hold in more general settings. We also prove a new type of limit result.
-
作者：Berman, Simeon M.
作者单位：New York University
摘要：Let Z be a normal random vector in R-k and let 1 be the element of R-k with equal components 1. Let X be a random variable that is independent of Z and consider the sum Z + X 1. The latter has a normal distribution in Rk if and only if X has a normal distribution in R1. The first result of this paper is a formula for a uniform bound on the difference between the density function of Z + X1 and the density function in the case where X has a suitable normal distribution. This is applied to a prob...
-
作者：Frieze, Alan; Kannan, Ravi; Polson, Nick
作者单位：Carnegie Mellon University; Telcordia Technologies; Carnegie Mellon University; University of Chicago
-
作者：Clouet, J. F.; Fouque, J. P.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：This paper investigates the deformation of an acoustic pulse travelling in a slab of random medium when its width is large compared to the size of the random inhomogeneities of the medium. A limit theorem is shown that explains how the shape of the transmitted pulse can be obtained as a result of a deterministic Gaussian convolution of the initial pulse. Since the random fluctuations are not supposed to be small, this gives a new rigorous formulation of the O'Doherty-Anstey result, which is we...
