Lévy Processes,Phase-Type Distributions,and Martingales

Lévy processes are defined as processes with stationary independent increments and have become increasingly popular as models in queueing, finance, etc.; apart from Brownian motion and compound Poisson processes, some popular examples are stable processes, variance gamma processes, CGMY Lévy processes (tempered stable processes), NIG (normal inverse Gaussian) Lévy processes, and hyperbolic Lévy processes. We consider here a dense class of Lévy processes, compound Poisson processes with phase-type jumps in both directions and an added Brownian component. Within this class, we survey how to explicitly compute a number of quantities that are traditionally studied in the area of Lévy processes, in particular two-sided exit probabilities and associated Laplace transforms, the closely related scale function, one-sided exit probabilities and associated Laplace transforms coming up in queueing problems, and similar quantities for a Lévy process with reflection in 0. The solutions are in terms of roots to polynomials, and the basic equations are derived by purely probabilistic arguments using martingale optional stopping; a particularly useful martingale is the so-called Kella-Whitt martingale. Also, the relation to fluid models with a Brownian component is discussed.     

The Henderson Smoother in Reproducing Kernel Hilbert Space

The Henderson smoother has been traditionally applied for trend-cycle estimation in the context of nonparametric seasonal adjustment software officially adopted by statistical agencies. This study introduces a Henderson third-order kernel representation by means of the reproducing kernel Hilbert space (RKHS) methodology. Two density functions and corresponding orthonormal polynomials have been calculated. Both are shown to give excellent representations for short- and medium-length filters. Theoretical and empirical comparisons of the Henderson third-order kernel asymmetric filters are made with the classical ones. The former are shown to be superior in terms of signal passing, noise suppression, and revision size.     

The consistency of model selection for dynamic Semi-varying coefficient models with autocorrelated errors

The consistency of model selection criterion BIC has been well and widely studied for many nonlinear regression models. However, few of them had considered models with lag variables as regressors and auto-correlated errors in time series settings, which is common in both linear and nonlinear time series modeling. This paper studies a dynamic semi-varying coefficient model with ARMA errors, using an approach based on spectrum analysis of time series. The consistency property of the proposed model selection criteria is established and an implementation procedure of model selection is proposed for practitioners. Simulation studies have also been conducted to numerically show the consistency property.     

线性方程组的单调收敛

本文讨论了线性方程组Au=b的单调收敛性,给出了某些线性方程组Au=b占之单调收敛性的判定条件.     

Multitaper testing of spectral lines and the detection of the solar rotation frequency and its harmonics

We develop statistical testing methodology for closely spaced spectral lines based on multitaper spectrum estimates and apply it to a time series of solar magnetic field magnitude data recorded by the Ulysses spacecraft. The test is formulated through complex-valued weighted least squares. Using this test in combination with the test for well-separated lines, we can accurately detect the solar equatorial rotation frequency of the sun, and its harmonics, from data recorded by Ulysses's magnetometer at solar mid-latitudes; this is a potentially important result for solar physicists, since it has implications for the structure and dynamics of magnetic fields in the solar corona.     

Semiparametric estimation of spatial long-range dependence

Estimation of the long-range dependence parameter in spatial processes using a semiparametric approach is studied. An extended formulation of the averaged periodogram method proposed in Robinson [1994. Semiparametric analysis of long memory time series. Ann. Statist. 22, 515–539] is derived, considering a certain homogeneous and isotropic behaviour of the spectral distribution in the low frequencies. The weak consistency of the estimator proposed is proved.     

一类M-矩阵阿达玛积最小特征根的下界

讨论一个 M- 矩阵与另一个 M- 矩阵的逆的阿达玛积的最小特征根,证明了对任一矩阵B,如果 B- 1 的主对角线元素的值相等,则q( A‘B- 1) > 1n ·q( A)q( B) .     

冰箱压缩机噪声分析及降噪措施的研究

采用频谱分析技术,研究了QD55A冰箱压缩机主要噪声来源,提出了以减小压缩机气流脉动性噪声为主的降噪措施。经批量生产测试验证,噪声下降4 dB。     

迭代法迭代阵谱半径新上界

引用双严格对角占优的概念,针对线性方程组bAx=在求数值解时常用的迭代方法,给出了Jacobi和Gauss-Seidel迭代法迭代阵谱半径的新上界,该新上界优于严格对角占优矩阵条件下得到的已有的结果,是已有结果在更广泛矩阵类条件下的推广,对相应迭代法迭代阵谱半径的估计更加精确。最后给出了数值例子说明所给结果的优越性。     

既有线提速小半径曲线平面改造方法研究

为了满足铁路运能增加和现代经济快速发展的需求,新建铁路的同时对既有线铁路的提速改造也是非常必要的,而平面改造中小半径曲线已成为既有线提速的一个瓶颈问题。以“哈尔滨至漠河铁路扩能改造工程”加格达奇至塔河段的方案研究为例,讨论了关于既有线提速改造的设计原则及思路;结合该区段工程的设计改造过程,根据铁路的平面既有现状及特点,重点介绍了平面改造中小半径曲线的改造方法。结果表明:改造完成后的铁路平面条件能很好地满足该区段的提速要求,取得了良好的效果,为今后既有铁路提速改造提供了一定的参考。