-
作者：Klüppelberg, C; Pergamenchtchikov, S
作者单位：Technical University of Munich; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an autoregressive process with ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary order.
-
作者：Huber, M
作者单位：Duke University; Duke University
摘要：Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably accurate and construction of perfect sampling algorithms when used in conjunction with protocols such as coupling from the past. Perfect sampling algorithms generate variates exactly from the target distribution without the need to know the mixing time of a...
-
作者：Zwart, B; Borst, S; Mandjes, M
作者单位：Eindhoven University of Technology; Centrum Wiskunde & Informatica (CWI)
摘要：We consider a fluid queue fed by multiple On-Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a dominant subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a minima...
-
作者：Baccelli, F; Foss, S
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Inria; Heriot Watt University
摘要：A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework, which was first introduced to derive the stability region for stochastic networks with stationary and ergodic driving sequences, is revisited. It contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multi-server queues, and various classes of stochastic Pet...
-
作者：Hugonnier, J; Kramkov, D
作者单位：Universite de Montreal; HEC Montreal; Universite de Montreal; Carnegie Mellon University
摘要：In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization problem not only the initial capital but also the number of units of the random endowments. We show that this approach leads to a dual problem, whose solution is always attained in the space of random variables. In particular, this technique does not require th...
-
作者：Miyazawa, M
作者单位：Tokyo University of Science
摘要：Motivated by a risk process with positive and negative premium rates, we consider a real-valued Markov additive process with finitely many background states. This additive process linearly increases or decreases while the background state is unchanged, and may have upward jumps at the transition instants of the background state. It is known that the hitting probabilities of this additive process at lower levels have a matrix exponential form. We here study the hitting probabilities at upper le...
-
作者：Kratz, MF; Picco, P
作者单位：Universite Paris Cite; Aix-Marseille Universite
摘要：In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented. Then we give a precise description of the support of the Gibbs measure below the critical temperature.
-
作者：Panholzer, A; Prodinger, H
作者单位：Technische Universitat Wien; University of Witwatersrand
摘要：This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normalized) spanning tree size converges in law to the Normal distribution. The special case p = 2 reproves the recent result (obtained by the contraction method by Mahmoud and Neininger [Ann. Appl. Probab. 13 (2003) 253-276]), that the distribution of distances in random binary search trees has a Gaussian limit law. In the...
-
作者：Delcoigne, F; De La Fortelle, A
作者单位：Electricite de France (EDF); Inria
摘要：We are interested in analyzing the effect of bandwidth sharing for telecommunication networks. More precisely, we want to calculate which routes are bottlenecks by means of large deviations techniques. The method is illustrated in this paper on a star network, where the bandwidth is shared between customers according to the so-called min policy. We prove a sample path large deviation principle for a rescaled process n(-1) Q(nt), where Q(t) represents the joint number of connections at time t. ...
-
作者：Lefebvre, M
作者单位：Universite de Montreal; Polytechnique Montreal
摘要：Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled until it reaches either end of the interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost equal to zero (resp. a large constant) if the process exits the interval through its left (resp....
