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• Spectral theory and limit theorems for geometrically ergodic Markov processes AI翻译
  作者：Kontoyiannis, I; Meyn, SP
  作者单位：Brown University; Brown University; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Consider the partial sums {S-t} of a real-valued functional F(phi)(t)) of a Markov chain {(phi(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the following conclusions are obtained: Spectral theory. Well-behaved solutions f can be constructed for the multiplicative Poisson equation (e(alphaF) P)f =lambdaf, where P is the transition kernel of the Markov chain and alpha is an element of C is a constant....
• Ruin problem and how fast stochastic processes mix AI翻译
  作者：Embrechts, P; Samorodnitsky, G
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Cornell University
  摘要：The recent increasing interplay between actuarial and financial mathematics has led to a surge in risk theoretic modeling. Especially actuarial ruin models under fairly general conditions on the underlying risk process have become a focus of attention. Motivated by applications such as the modeling of operational risk losses in financial risk management, we investigate the stability of classical asymptotic ruin estimates when claims are heavy, and this under variability of the claim intensity ...
• Distribution of distances in random binary search trees AI翻译
  作者：Mahmoud, HM; Neininger, R
  作者单位：George Washington University; McGill University
  摘要：We investigate random distances in a random binary search tree. Two types of random distance are considered: the depth of a node randomly selected from the tree, and distance between randomly selected pairs of nodes. By a combination of classical methods and modern contraction techniques we arrive at a Gaussian limit law for normed random distances between pairs. The exact forms of the mean and variance of this latter distance are first derived by classical methods to determine the scaling pro...
• Brownian models of open processing networks: Canonical representation of workload (vol 10, pg 75, 2000) AI翻译
  作者：Harrison, JM
  作者单位：Stanford University
• The maximum on a random time interval of a random walk with long-tailed increments and negative drift AI翻译
  作者：Foss, S; Zachary, S
  作者单位：Heriot Watt University
  摘要：We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen, simplify its proof and give some converses.
• Continuous-time controlled Markov chains AI翻译
  作者：Guo, XP; Hernández-Lerma, O
  作者单位：Sun Yat Sen University; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; Instituto Politecnico Nacional - Mexico
  摘要：This paper concerns studies on continuous-time controlled Markov chains, that is, continuous-time Markov decision processes with a denumerable state space, with respect to the discounted cost criterion. The cost and transition rates are allowed to be unbounded and the action set is a Borel space. We first study control problems in the class of deterministic stationary policies and give very weak conditions under which the existence of epsilon-optimal (epsilon greater than or equal to 0) polici...
• When can one detect overdominant selection in the infinite-alleles model? AI翻译
  作者：Joyce, P; Krone, SM; Kurtz, TG
  作者单位：University of Idaho; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
  摘要：One of the goals of this paper is to show that the infinite-alleles model with overdominant selection looks like the neutral infinite-alleles model when the selection intensity and mutation rate get large together. This rather surprising behavior was noticed by Gillespie (1999) in simulations. To make rigorous and refine Gillespie's observations, we analyze the limiting behavior of the likelihood ratio of the stationary distributions for the model under selection and neutrality, as the mutatio...
• Multiple-input heavy-traffic real-time queues AI翻译
  作者：Kruk, L; Lehoczky, J; Shreve, S; Yeung, SN
  作者单位：Maria Curie-Sklodowska University; Carnegie Mellon University; Carnegie Mellon University; AT&T
  摘要：A single queueing station that serves K input streams is considered. Each stream is an independent renewal process, with customers having random lead times. Customers are served by processor sharing across streams. Within each stream, two disciplines are considered-earliest deadline first and first-in, first-out. The set of current lead times of the K streams is modeled as a K-dimensional vector of random counting measures on R, and the limit of this vector of measure-valued processes is obtai...
• Strong approximation of the empirical process of GARCH sequences (vol 11, pg 789, 2001) AI翻译
  作者：Berkes, I; Horváth, L
  作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Utah System of Higher Education; University of Utah
• Fluid and heavy traffic diffusion limits for a generalized processor sharing model AI翻译
  作者：Ramanan, K; Reiman, MI
  作者单位：AT&T; Alcatel-Lucent; Lucent Technologies
  摘要：Under fairly general assumptions on the arrival and service time processes, we prove fluid and heavy traffic limit theorems for the unfinished work, queue length, sojourn time and waiting time processes associated with a single station multiclass generalized processor sharing model. The fluid limit of the unfinished work process is characterized by the Skorokhod map associated with a Skorokhod problem formulation of the generalized processor sharing model, while the heavy traffic diffusion lim...