The Annals of Applied Probability

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• Exponential penalty function control of loss networks AI翻译
  作者：Iyengar, G; Sigman, K
  作者单位：Columbia University
  摘要：We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to to...
• Mixing times of lozenge tiling and card shuffling Markov chains AI翻译
  作者：Wilson, DB
  作者单位：Microsoft
  摘要：We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, Randall and Sinclair to generate random tilings of regions by lozenges. For an l x l region we bound the mixing time by O(l(4) log l), which improves on the previous bound of O(l(7)), and we show the new boun...
• Asymptotic genealogy of a critical branching process AI翻译
  作者：Popovic, L
  作者单位：University of California System; University of California Berkeley
  摘要：Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribut...
• Moments and tails in monotone-separable stochastic networks AI翻译
  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...
• Elementary bounds on Poincare and log-Sobolev constants for decomposable Markov chains AI翻译
  作者：Jerrum, M; Son, JB; Tetali, P; Vigoda, E
  作者单位：University of Edinburgh; University System of Georgia; Georgia Institute of Technology; University of Chicago
  摘要：We consider finite-state Markov chains that can be naturally decomposed into smaller projection and restriction chains. Possibly this decomposition will be inductive, in that the restriction chains will be smaller copies of the initial chain. We provide expressions for Poincare (resp. log-Sobolev) constants of the initial Markov chain in terms of Poincare (resp. log-Sobolev) constants of the projection and restriction chains, together with further a parameter. In the case of the Poincare const...
• Practical drift conditions for subgeometric rates of convergence AI翻译
  作者：Douc, R; Fort, G; Moulines, E; Soulier, P
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; IMT - Institut Mines-Telecom; IMT Atlantique; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite Paris Saclay
  摘要：We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Anti. Appl. Probab. 12 (2002) 224-247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic ...
• Local limit theory and large deviations for supercritical branching processes AI翻译
  作者：Ney, PE; Vidyashankar, AN
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University System of Georgia; University of Georgia
  摘要：In this paper we study several aspects of the growth of a supercritical Galton-Watson process {Z(n) : n greater than or equal to 1}, and bring out some criticality phenomena determined by the Schroder constant. We develop the local limit theory of Z(n), that is, the behavior of P(Z(n) = v(n)) as v(n) NE arrow infinity, and use this to study conditional large deviations of {Y-Zn : n greater than or equal to 1}, where Y-n satisfies an LDP, particularly of {Z(n)(-1) Z(n+1) : n greater than or equ...
• When can the two-armed bandit algorithm be trusted? AI翻译
  作者：Lamberton, D; Pagès, G; Tarrès, P
  作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：We investigate the asymptotic behavior of one Version of the so-called two-armed bandit algorithm. It is an example of stochastic approximation procedure whose associated ODE has both a repulsive and an attractive equilibrium, at which the procedure is noiseless. We show that if the gain parameter is constant or goes to 0 not too fast, the algorithm does fall in the noiseless repulsive equilibrium with positive probability, whereas it always converges to its natural attractive target when the ...
• AIMD algorithms and exponential functionals AI翻译
  作者：Guillemin, F; Robert, P; Zwart, B
  作者单位：Orange SA; Eindhoven University of Technology
  摘要：The behavior of a connection transmitting packets into a network according to a general additive-increase multiplicative-decrease (AIMD) algorithm is investigated. It is assumed that loss of packets occurs in clumps. When a packet is lost, a certain number of subsequent packets are also lost (correlated losses). The stationary behavior of this algorithm is analyzed when the rate of occurrence of clumps becomes arbitrarily small. From a probabilistic point of view, it is shown that exponential ...
• Optimal scaling of mala for nonlinear regression AI翻译
  作者：Breyer, LA; Piccioni, M; Scarlatti, S
  作者单位：Lancaster University; G d'Annunzio University of Chieti-Pescara; Sapienza University Rome
  摘要：We address the problem of simulating efficiently from the posterior distribution over the parameters of a particular class of nonlinear regression models using a Langevin-Metropolis sampler. It is shown that as the number N of parameters increases, the proposal variance must scale as N-1/3 in order to converge to a diffusion. This generalizes previous results of Roberts and Rosenthal [J. R. Stat. Soc. Ser B Stat. Methodol. 60 (1998) 255-268] for the i.i.d. case, showing the robustness of their...