21 research outputs found

    Convergence in law to operator fractional Brownian motions

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    In this paper, we provide two approximations in law of operator fractional Brownian motions. One is constructed by Poisson processes, and the other generalizes a result of Taqqu (1975)

    Random Walks and Subfractional Brownian Motion

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    In this article, we show a result of approximation in law to subfractional Brownian motion, with H>12H>\frac{1}{2}, in the Skorohod topology. The construction of these approximations is based on a sequence of I.I.D random variable

    Convergence rates in precise asymptotics for a kind of complete moment convergence

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    In Liu and Lin (Statist. Probab. Letters, 2006), they introduced a kind of complete moment convergence which includes complete convergence as a special case. Inspired by the study of complete convergence, in this paper, we study the convergence rates of the precise asymptotics for this kind of complete moment convergence and get the corresponding convergence rates.Comment: 16 page

    Stationary Distributions for Two-Dimensional Sticky Brownian Motions: Exact Tail Asymptotics and Extreme Value Distributions

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    In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and mathematical finance. For example, a sticky Brownian motion can be used to model a storage system.with exceptional services. In this paper, we focus on stationary distributions for sticky Brownian motions. The main results obtained here include tail asymptotic properties in boundary stationary distributions, marginal distributions, and joint distributions. The kernel method, copula concept and extreme value theory are main tools used in our analysis.Comment: 32 page

    Limit theorems for functionals of Gaussian vectors

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    Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar processComment: Front. Math. China, 201

    Exact tail asymptotics for a discrete-time preemptive priority queue

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    In this paper, we consider a discrete-time preemptive priority queue with different service rates for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers' arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated. In this model, we focus on the characterization of exact tail asymptotics for the joint stationary distribution of the queue length of the two classes of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and kernel method, we get an explicit expression of exact tail asymptotics along the low-priority queue direction, as well as along the high-priority queue direction

    Operator Fractional Brownian Sheet and Martingale Differences

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    In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences

    Exact tail asymptotics for a three dimensional Brownian-driven tandem queue with intermediate inputs

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    The semimartingale reflecting Brownian motion (SRBM) can be a heavy traffic limit for many server queueing networks. Asymptotic properties for stationary probabilities of the SRBM have attracted a lot of attention recently. However, many results are obtained only for the two-dimensional SRBM. There is only little work related to higher dimensional (3\geq 3) SRBMs. In this paper, we consider a three dimensional SRBM: A three dimensional Brownian-driven tandem queue with intermediate inputs. We are interested in tail asymptotics for stationary distributions. By generalizing the kernel method and using copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and the joint stationary distribution.Comment: 35 page

    Elastic Net Procedure for Partially Linear Models

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    Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. By a simulation study, we show that the strongly correlated variables problem can be better handled by the Elastic Net procedure than Lasso, ALasso and Ridge. Based on an empirical analysis, we can get that the Elastic Net procedure is particularly useful when the number of predictors pp is much bigger than the sample size nn.Comment: arXiv admin note: text overlap with arXiv:0908.1836 by other author

    Single index regression models with randomly left-truncated data

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    In this paper, based on the kernel estimator proposed by Ould-Said and Lemdani (Ann. Instit. Statist. Math. 2006), we develop some new generalized M-estimator procedures for single index regression models with left-truncated responses. The consistency and asymptotic normality of our estimators are also established. Some simulation studies are given to investigate the finite sample performance of the proposed estimators.Comment: 17 page
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