一种估算马尔柯夫状态转移概率矩阵的新方法

在现有文献研究的基础上,对马尔柯夫状态转移概率矩阵估算方法又作了进一步研究,根据马尔柯夫状态转移概率矩阵的性质和特点,提出了一种新的估算方法.方法首先构造了一个以相对误差绝对值之和最小为目标,以某一状态转移到其他状态的概率之和等于1以及状态转移概率不小于零为约束条件的优化模型.在此基础上,通过变量替换,将该模型转化为线性规划模型.由于线性规划模型不仅能够求得解析解,而且有现成的求解软件,因此不但便于问题求解,而且更加方便、可靠.最后进行了示例计算,验证了给出的马尔柯夫状态转移概率矩阵优化算法的可行性和正确性.

A New Method to Estimate Markov State Transition Probability Matrix

Based on the existed studies,this article has further studied the optimization algorithm of Markova Transition Matrix,according to the nature and specialty of the Markova Transition Matrix.Then one new estimated method is given.First of all,establish an optimization model which goal is the minimum of the sum of absolute value of relative error.There are two constraint conditions,one is the sum of probabiUty shift from one state to another state,and the other is the state transition probability not less than zero.Secondly,through the variable substitution,the model is transformed into linear programming model.The advantage is that using mature software to obtain the reliable Markova Transition Matrix analytical solution quickly and easily.At last,example calculation is given to check the new estimate method and provide its feasibility and exactness.