马氏链首达时间反问题中矩的估计及其性能分析

Estimation method and its properties of moments of first passage time for Markov chains in reverse problems

提出了马氏链的反向问题中，在独立加性高斯有色随机噪声背景下，估计Ｍａｒｋｏｖ链首达时间各阶矩的统计方法。利用累积量的性质，得出了带噪样本的ｋ阶矩仅与噪声的方差有关，而与噪声的其它任意阶矩无关，并证明了用该方法得到的估计值具有无偏性和强相合性的统计性能。通过一个数值例子仿真了连续时间参数Ｍａｒｋｏｖ链模型的构造过程，得到的首达时间各阶矩的估计值及其分布函数的Ｌ－Ｓ变换比去噪处理前更接近无噪声情况，在理论和实验两方面验证了该方法的有效性。

This paper presents a statistical approach for estimating the moments of the first passage time for Markov chains under a background of independent additive Gaussian colored noise in the reverse problem for Markov chains. By using the comulents, it is obtained that the k order moment of the noisy samples is only related to the variance of the noise, and is independent to any other order moments of the noise. It can also be proved that the estimators obtained from this algorithm have the properties of unbiasedness and congruence. A numerical simulation is performed for constructing a Markov chain of continuous time parameters. The results show the validity of this algorithm.