全面理解运动和矛盾的关系

运动和矛盾的关系问题,是辩证法中的根本问题,应当从运动的源泉、本质和表现形式三个方面来考察。矛盾是事物运动变化发展的内容、源泉、动力、原因,而运动则是矛盾的表现、存在形式及实现。运动的本质是时间和空间的直接统一,是时间空间的非间断性和间断性的统一。无论是同一种运动形式,还是不同运动形式,运动的表现形式都离不开矛盾、充满着矛盾。     

Statistical inference on the drift parameter in fractional Brownian motion with a deterministic drift

In statistical inference on the drift parameter a in the fractional Brownian motion W^H_t with the Hurst parameter H ∈ (0, 1) with a constant drift Y^H_t = at + W^H_t, there is a large number of options how to do it. We may, for example, base this inference on the properties of the standard normal distribution applied to the differences between the observed values of the process at discrete times. Although such methods are very simple, it turns out that more appropriate is to use inverse methods. Such methods can be generalized to non constant drift. For the hypotheses testing about the drift parameter a, it is more proper to standardize the observed process, and to use inverse methods based on the first exit time of the observed process of a pre-specified interval until some given time. These procedures are illustrated, and their times of decision are compared against the direct approach. Other generalizations are possible when the random part is a symmetric stochastic integral of a known, deterministic function with respect to fractional Brownian motion.     

ANOVA models for Brownian motion

We investigate longitudinal models having Brownian-motion covariance structure. We show that any such model can be viewed as arising from a related “timeless” classical linear model where sample sizes correspond to longitudinal observation times. This relationship is of practical impact when there are closed-form ANOVA tables for the related classical model. Such tables can be directly transformed into the analogous tables for the original longitudinal model. We in particular provide complete results for one-way fixed and random effects ANOVA on the drift parameter in Brownian motion, and illustrate its use in estimating heterogeneity in tumor growth rates.     

Some asymptotic results for the integrated empirical process with applications to statistical tests

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975 Komlós, J., Major, P., Tusnády, G. (1975). An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32:111–131.[Crossref], [Web of Science ®] , [Google Scholar])'s results. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial-sum process representation of the integrated empirical process.     

Karhunen–Loeve expansion for the additive detrended Brownian motion

In this article, we obtain the Karhunen–Loeve expansion and Pythagorean type distribution identities for the additive detrended Brownian motion. As applications, the corresponding Laplace transform and small-deviation asymptotic behavior for the L₂ norm are given.     

Slowing time: Markov-modulated Brownian motions with a sticky boundary

We define a new family of stochastic processes called Markov modulated Brownian motions with a sticky boundary at zero. Intuitively, each process is a regulated Markov-modulated Brownian motion whose boundary behavior is modified to slow down at level zero.

To determine the stationary distribution of a sticky MMBM, we follow a Markov-regenerative approach similar to the one developed with great success in the context of quasi-birth-and-death processes and fluid queues. Our analysis also relies on recent work showing that Markov-modulated Brownian motions arise as limits of a parametrized family of fluid queues.     

口径面天线辐射近区场强计算

利用一种新的天线口径场积分的近似算法和几何绕射理论,并结合实际工程中天线的计算实例,对口径面天线的近区场进行计算,提高了计算的速度,又保证了计算结果的准确性。结果表明,该方法是处理天线辐射近区场强以及电磁兼容问题的一种有力工具。     

Bootstrapping with auxiliary information

In the nonparametric setting, the standard bootstrap method is based on the empirical distribution function of a random sample. The author proposes, by means of the empirical likelihood technique, an alternative bootstrap procedure under a nonparametric model in which one has some auxiliary information about the population distribution. By proving the almost sure weak convergence of the modified bootstrapped empirical process, the validity of the proposed bootstrap procedure is established. This new result is used to obtain bootstrap confidence bands for the population distribution function and to perform the bootstrap Kolmogorov test in the presence of auxiliary information. Other applications include bootstrapping means and variances with auxiliary information. Three simulation studies are presented to demonstrate the performance of the proposed bootstrap procedure for small samples.     

A Latent Process Model for Joint Modeling of Events and Marker

The paper formulates joint modeling of a counting process and a sequence of longitudinal measurements, governed by a common latent stochastic process. The latent process is modeled as a function of explanatory variables and a Brownian motion process. The conditional likelihood given values of the latent process at the measurement times, has been drawn using Brownian bridge properties; then integrating over all possible values of the latent process at the measurement times leads to the desired joint likelihood. An estimation procedure using joint likelihood and a numerical optimization is described. The method is applied to the study of cognitive decline and Alzheimer's disease.     

Excursion and meander in random walk

Bernoulli bridge, excursion and meander are defined on the symmetric random walk similarly to Brownian bridge, excursion and meander (cf. Chung 1976). Distributions of certain characteristics defined on these Bernoulli processes, which are of a combinatorial nature, and their limits are obtained. Using weak convergence, these derivations give a verification of some of the earlier results on Brownian excursion and Brownian meander, as well as some new results.