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作者：Mason, David M.; Polonik, Wolfgang
作者单位：University of Delaware; University of California System; University of California Davis
摘要：We establish the asymptotic normality of the G-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator. Our proof will highlight the efficacy of Poissonization methods in the treatment of large sample theory problems of this kind.
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作者：Jara, Milton; Komorowski, Tomasz; Olla, Stefano
作者单位：Universite PSL; Universite Paris-Dauphine; Maria Curie-Sklodowska University
摘要：Consider a Markov chain {X(n)}(n >= 0) with an ergodic probability measure pi. Let be a function on the state space of the chain, with a-tails with respect to pi, alpha is an element of (0, 2). We find sufficient conditions on the probability transition to prove convergence in law of N(1/alpha) Sigma(N)(n) Psi(X(n)) to an a-stable law. A martingale approximation approach and a coupling approach give two different sets of conditions. We extend these results to continuous time Markov jump proces...
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作者：Albenque, Marie
作者单位：Universite Paris Cite
摘要：In the literature, most of the results about the enumeration of directed animals on lattices via gas considerations are obtained by a formal passage to the limit of enumeration of directed animals on cyclical versions of the lattice. Here we provide a new point of view on this phenomenon. Using the gas construction given in [Electron. J. Combin. (2007) 14 R71], we describe the gas process on the cyclical versions of the lattices as a cyclical Markov chain (roughly speaking, Markov chains condi...
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider Kac's random walk on n-dimensional rotation matrices, where each step is a random rotation in the plane generated by two randomly picked coordinates. We show that this process converges to the Haar measure on SO(n) in the L-2 transportation cost (Wasserstein) metric in O(n(2) In n) steps. We also prove that our bound is at most a O(In n) factor away from optimal. Previous bounds, due to Diaconis/Saloff-Coste and Pak/Sidenko, had extra powers of n and held only for L-1 transportatio...
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作者：Lahiri, S. N.; Sun, S.
作者单位：Texas A&M University System; Texas A&M University College Station; University System of Ohio; Wright State University Dayton
摘要：This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n(-1/2)) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics a...
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作者：Meilijson, Isaac
作者单位：Tel Aviv University
摘要：Consider a random walk whose (light-tailed) increments have positive mean. Lower and upper bounds are provided for the expected maximal value of the random walk until it experiences a given drawdown d. These bounds, related to the Calmar ratio in finance, are of the form (exp{alpha d}-1)/alpha and (K exp{alpha d}-1)/alpha for some K > 1, in terms of the adjustment coefficient alpha (E[exp{-alpha X}] = 1) of the insurance risk literature. Its inverse 1/alpha has been recently derived by Aumann ...
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作者：Jourdain, Benjamin; Lelong, Jerome
作者单位：Institut Polytechnique de Paris; ENSTA Paris
摘要：Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of importance sampling for normal random vectors. Unlike stochastic approximation, which requires very fine tuning in practice, we propose to use sample average approximation and deterministic optimization techniques to devise a robust and fully automatic variance reduc...
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作者：Ohashi, Alberto
作者单位：Universidade Estadual de Campinas
摘要：In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fract...
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作者：Han, Guangyue; Marcus, Brian
作者单位：University of Hong Kong; University of British Columbia
摘要：We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117-122], we derive an asymptotic formula (when the noise parameter is small) for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a BSC. Using this res...
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作者：Awad, Hernan; Glynn, Peter
作者单位：University of Miami; Stanford University
摘要：We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value b, we provide the limiting distribution for the amount of time that the workload process spends above level b over the busy cycle straddling the origin, as b -> infinity. Our results can be interpreted as showing that long delays occur in large clumps of size of order b(2-1/H). The conditional limit result involves a finer scaling of the queueing...
