Semi-Markov Processes and Reliability
Semi-Markov Processes and Reliability
复制标题
DOI：
10.1007/978-1-4612-0161-8
复制
发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
N. Limnios;G. Oprișan
中科院分区：
文献类型：
--
作者：
N. Limnios;G. Oprișan
首先是马尔可夫性质。随机过程理论可以被视为概率论的扩展，它允许对系统随时间的演化进行建模。它不能像纯粹的数学一样被正确地理解，脱离了使其栩栩如生的经验和例子。当马尔可夫性质的思想被引入时，随机过程理论进入了一个深入发展的时期，而这个时期还没有结束。如果不使用马尔可夫过程这一强有力的工具，甚至不可能对更新过程进行认真的研究。现代马尔可夫过程理论起源于 A. A: 马尔可夫 (1856-1922) 对“连成一条链”的实验序列的研究，以及试图用数学方法描述称为布朗运动的物理现象的尝试。后来，马尔可夫型随机过程的许多推广（实际上是马尔可夫性质的各种弱化）被提出。其中一些已经导致了新的随机过程类别和有用的应用。让我们提一下其中的一些： 具有完整连接的系统 [90, 91, 45, 86]； K 相关马尔可夫过程 [44]；半马尔可夫过程等等。半马尔可夫过程概括了更新过程和马尔可夫跳跃过程，并且有许多应用，特别是在可靠性方面。
At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments" connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia bility.