By using the idea of taking states from model and model forecast,a design method is presented for discrete MRACS following reference sequence that is suitable for delay system.

3 earthquake and the distinct anomalies of its sequence parameters, we studied the regulation of strong earthquake activity in the Xiaojiang fault, the relation between concentrated moderate earthquake cluster activity and tectonic activity, and the stress field in and around the Xiaojiang fault after the Huize earthquake.

When residual GM(1,1) model does not match requisition,we can make use of the residual sequence which establishes GM(1,1) model to modify primary model,to raise the accuracy.

In this paper, a method of process quality diagnosis using hypothesis testing for residual sequence of ARMA innovation model estimation error by recursive maximum likelihood method was studied.

This paper,uses the property of being uniformly integrable to truncate the random variable sequences,and under the condition of φ(x)x↑,φ(x)x2↓,obtain a weak law of large number of martingale difference sequences by the weak convergence theorem.

We use least squares and least neighhor weight function to define the estimations and (t) for parametric β and nonparametric g(t) of semiparametric regression model, and obtain their r th mean consistency under martingale difference sequences.

Positively associated random variables (PA) and Martingale difference sequences arevery important cases in the dependent random variables.

The extension and application of convergence theorem about martingale difference sequence;

Convergence rate of the parametric estimate of the regression model of half-paramter under error being martingale difference sequence;

Presents some results for weighted sums of multidimensionally indexed and stochastically dominated random variables using orthogonality of martingale difference sequence, which extend the related results of AndrèAdler and Andrew Rosalsky.