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作者：Jara, Milton; Komorowski, Tomasz; Olla, Stefano
作者单位：Universite PSL; Universite Paris-Dauphine; Maria Curie-Sklodowska University
摘要：Consider a Markov chain {X(n)}(n >= 0) with an ergodic probability measure pi. Let be a function on the state space of the chain, with a-tails with respect to pi, alpha is an element of (0, 2). We find sufficient conditions on the probability transition to prove convergence in law of N(1/alpha) Sigma(N)(n) Psi(X(n)) to an a-stable law. A martingale approximation approach and a coupling approach give two different sets of conditions. We extend these results to continuous time Markov jump proces...
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作者：Awad, Hernan; Glynn, Peter
作者单位：University of Miami; Stanford University
摘要：We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value b, we provide the limiting distribution for the amount of time that the workload process spends above level b over the busy cycle straddling the origin, as b -> infinity. Our results can be interpreted as showing that long delays occur in large clumps of size of order b(2-1/H). The conditional limit result involves a finer scaling of the queueing...
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作者：Hitczenko, Pawel; Wesolowski, Jacek
作者单位：Drexel University; Warsaw University of Technology
摘要：We consider the tail behavior of random variables R which are solutions of the distributional equation R (d)= Q + M R, where (Q. M) is independent of R and vertical bar M vertical bar <= 1. Goldie and Grubel showed that the tails of R are no heavier than exponential and that if Q is bounded and M resembles near I the uniform distribution, then the tails of R are Poissonian. In this paper, we further investigate the connection between the tails of R and the behavior of M near 1. We focus on the...
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作者：Eder, Irmingard; Klueppelberg, Claudia
作者单位：Technical University of Munich; Technical University of Munich
摘要：For the sum process X = X-1 + X-2 of a bivariate Levy process (X-1, X-2) with possibly dependent components, we derive a quintuple law describing the first upwards passage event of X over a fixed barrier, caused by a jump, by the joint distribution of five quantities: the time relative to the time of the previous maximum, the time of the previous maximum, the overshoot, the undershoot and the undershoot of the previous maximum. The dependence between the jumps of X-1 and X-2 is modeled by a Le...
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作者：Graham, Carl; Robert, Philippe
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes of the route. Since several classes of connections going through the nodes of the network are considered, an original mean-field result in a multi-class context is established. It is shown that, as the number of ...
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We place ourselves in the setting of high-dimensional statistical inference, where the number of variables p in a data set of interest is of the same order of magnitude as the number of observations n. More formally, we study the asymptotic properties of correlation and covariance matrices, in the setting where p/n -> rho is an element of (0, infinity), for general population covariance. We show that, for a large class of models studied in random matrix theory, spectral properties of large-dim...
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作者：Chow, Pao-Liu
作者单位：Wayne State University
摘要：The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain D subset of R-d for d <= 3. Under appropriate conditions on the initial data, the nonlinear term and the noise intensity is proved in Theorem 3.1 that the L-2-norm of the solution will blow up at a finite time in the mean-square sense. An example is given to show an application of the theorem.
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作者：Zitkovic, Gordan
作者单位：University of Texas System; University of Texas Austin
摘要：We propose a mathematical framework for the study of a family of random fields-called forward performances-which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the or...
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作者：Walton, N. S.
作者单位：University of Cambridge
摘要：We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that...
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作者：Talreja, Rishi; Whitt, Ward
作者单位：Columbia University
摘要：We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding argument shows that the abandonment does not affect waiting-time processes. If instead the system is overloaded, as in the efficiency-driven (ED) regime, following Mandelbaum et al. [Proceedings of the Thirty-Seventh Annual Allerton Conference on Communicat...
