马尔可夫过程的传导转移概率及工程研究应用

The transfer probability of Markov process and its application in engineering research

将可拓学理论和方法首次应用到马尔可夫过程的研究中,给出了过程元和过程元概率函数的概念,将相关分析原理和可拓变换用于对马尔可夫过程的一步传导转移概率函数的研究.给出了马尔可夫过程在参变量取某值时的一步转移过程元和一步转移概率函数的概念并利用相关性、可拓变换和传导变换等对其进行了研究.实例分析表明:该方法可为一类涉及马尔可夫过程的矛盾问题提供一种新的形式化解决途径,丰富了可拓学在随机过程领域研究中的理论.

The extension theory and method are applied to the study of Markov processes for the first time.Gives the concept of process element and process element probability function,the correlation analysis principle and extension transformation were used to study the probability function of the step conduction Markov process transfer,given the Markov process in the concept of a step transfer element taking values of a certain value and one step transition probability function.In this paper,we use the correlation,extension transformation and conduction transformation to study the one-step conduction transfer process element and the one-step transfer probability function.The case study shows that this method can provide a new way to solve the problem of a class of Markov processes.