Adjoining Batch Markov Arrival Processes of a Markov Chain

A batch Markov arrival process（BMAP） X^＊=（N, J） is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper,a new and inverse problem is proposed firstly： given a Markov chain J, can we deploy a process N such that the 2-dimensional process X^＊=（N, J） is a BMAP？ The process X^＊=（N, J） is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed（i.i.d） random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic（D_k, k = 0, 1, 2· · ·）and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.

Novel parametric optimum processing method for airborne radar

In radar target detection, an optimum processor needs to automatically adapt its weights to the environment change. Conventionally, the optimum weights are obtained by substantial independently and identically distributed (i.i.d.) interference samplings, which is not always realistic in an inhomogeneous clutter background of airborne radar. The lack of i.i.d. samplings will inevitably lead to performance deterioration for optimum processing. In this paper, a novel parametric adaptive processing method is proposed for airborne radar target detection based on the modified Doppler distributed clutter (DDC) model with contribution of clutter's internal motion. It is different from the conventional methods in that the adaptive weights are determined by two parameters of DDC model, i.e., angular center and spread. A low-complexity nonlinear operators approach is also proposed to estimate these parameters. Simulation and performance analysis are also provided to show that the proposed method can remarkably reduce the dependence of i.i.d. samplings and it is computationally efficient for practical use.

The laws of large numbers for Pareto-type random variables under sub-linear expectation

In this paper,some laws of large numbers are established for random variables that satisfy the Pareto distribution,so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space.Based on the Pareto distribution,we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.

Random Stabilization of Sampled-data Control Systems with Nonuniform Sampling

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.