The Annals of Applied Probability

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• Average optimality for continuous-time Markov decision processes in Polish spaces AI翻译
  作者：Guo, Xianping; Rieder, Ulrich
  作者单位：Sun Yat Sen University; Ulm University
  摘要：This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We first provide two optimality inequalities with opposed directions, and also give suitable conditions under which the existenc...
• The overhand shuffle mixes in Θ(n2log n) steps AI翻译
  作者：Jonasson, J
  作者单位：Chalmers University of Technology
  摘要：The overhand shuffle is one of the real card shuffling methods in the sense that some people actually use it to mix a deck of cards. A mathematical model was constructed and analyzed by Pemantle [J. Theoret. Probab. 2 (1989) 37-49] who showed that the mixing time with respect to variation distance is at least of order n(2) and at most of order n(2) log n. In this paper we use an extension of a lemma of Wilson [Ann. Appl. Probab. 14 (2004) 274-325] to establish a lower bound of order n(2) log n...
• On the ergodicity properties of some adaptive MCMC algorithms AI翻译
  作者：Andrieu, Christophe; Moulines, Eric
  作者单位：University of Bristol; IMT - Institut Mines-Telecom; IMT Atlantique
  摘要：In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the independent Metropolis-Hastings ...
• Lifshitz tails for spectra of Erdos-Renyi random graphs AI翻译
  作者：Khorunzhiy, O; Kirsch, W; Müller, P
  作者单位：Universite Paris Saclay; University of Gottingen; Ruhr University Bochum; Ruhr University Bochum
  摘要：We consider the discrete Laplace operator Delta((N)) on Erdos-Renyi random graphs with N vertices and edge probability p/N. We are interested in the limiting spectral properties of Delta((N)) as N -> infinity in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of A (N) exhibits a Lifshitz-tail behavior at the lower spectral edge E = 0.
• Asymptotic theorems of sequential estimation-adjusted urn models AI翻译
  作者：Zhang, LX; Hu, FF; Cheung, SH
  作者单位：Zhejiang University; Chinese University of Hong Kong; University of Virginia
  摘要：The Generalized Polya Urn (GPU) is I popular urn model which is widely used in many disciplines. In particular. it is extensively used in treatment allocation schemes in clinical trials. Ill this paper, we propose it sequential estimation-adjusted urn model (a nonhomogeneous GPU) which has a wide spectrum of applications. Because the proposed urn model depends oil sequential estimations of unknown parameters, the derivation of asymptotic properties is mathematically intricate and the correspon...
• Pinning of polymers and interfaces by random potentials AI翻译
  作者：Alexander, Kenneth S.; Sidoravicius, Vladas
  作者单位：University of Southern California
  摘要：We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. Disorder is introduced by, for example, having the interaction vary from one monomer to another, as a constant u plus i.i.d. mean-0 randomness. There is a critical value of u above which the polymer is pinned, placing a positive fraction of its monomers at 0 with high probability. This critical point may di...
• Asymptotic analysis of multiscale approximations to reaction networks AI翻译
  作者：Ball, Karen; Kurtz, Thomas G.; Popovic, Lea; Rempala, Greg
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Wisconsin System; University of Wisconsin Madison; University of Louisville
  摘要：A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. We consider approaches ...
• Adaptive Poisson disorder problem AI翻译
  作者：Bayraktar, Erhan; Dayanik, Savas; Karatzas, Ioannis
  作者单位：University of Michigan System; University of Michigan; Princeton University; Princeton University; Columbia University
  摘要：We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder time. Our objective is to design an alarm time which is adapted to the history of the arrival process and detects the disorder time as soon as possible. In previous solvable versions of the Poisson disorder problem, the arrival rate after the disorder has been assumed a known constant. In reality, how...
• A spatially explicit model for competition among specialists and generalists in a heterogeneous environment AI翻译
  作者：Lanchier, N.; Neuhauser, C.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：Competition is a major force in structuring ecological communities. The strength of competition can be measured using the concept of a niche. A niche comprises the set of requirements of an organism in terms of habitat, environment and functional role. The more niches overlap, the stronger competition is. The niche breadth is a measure of specialization: the smaller the niche space of an organism, the more specialized the organism is. It follows that, everything else being equal, generalists t...
• Complete corrected diffusion approximations for the maximum of a random walk AI翻译
  作者：Blanchet, Jose; Glynn, Peter
  作者单位：Harvard University; Stanford University
  摘要：Consider a random walk (S-n : n >= 0) with drift - mu and S-0 = 0. Assuming that the increments have exponential moments. negative mean. and are strongly nonlattice. we provide a complete asymptotic expansion (in powers of mu > 0) that corrects the diffusion approximation of the all time maximum M = max(n >= 0) S-n. Our results extend both the first-order correction of Siegmund [Adv in Appl. Probab. 11 (1979) 701-719] and the full asymptotic expansion provided in the Gaussian case by Chang and...