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作者：Li, DL; Rosalsky, A
作者单位：Lakehead University; State University System of Florida; University of Florida
摘要：Let (X-k,X-i;i >= 1, k >= 1) be an array of i.i.d. random variables and let {P-n;n >= 1} be a sequence of positive integers such that n/P-n is bounded away from 0 and infinity. For W-n = max1 <= i <= pn vertical bar Sigma(n)(k=1) Xk,iXk,j vertical bar and L-n = max1 <= i,< j <= pn,vertical bar P-i,j((n))vertical bar where p(i,j)((n)) denotes the Pearson correlation coefficient between (XI,i, - - -, Xn,i)' and (Xij, - - -, Xnj)', the limit laws W limn -> oo Wn/n alpha = 0 a.s. (alpha > 1/2), (i...
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作者：Piau, Didier
作者单位：Universite Claude Bernard Lyon 1; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population k is greater than a first threshold m(1) >= 1. If, furthermore, k is greater than a second threshold m(2) >= m(1), the normalized mean inverse population is at most 1/(k - m(2)). We express m(1) and m(2) as explicit functionals of the reproducing distribution, we discuss some analogues...
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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...
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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...
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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 ...
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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.
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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...
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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...
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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 ...
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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...
