几种典型随机过程的介绍与应用

随机过程的理论体系在我们的生活应用中十分常见，本文主要对两种典型的随机过程进行了介绍：泊松过程和马尔可夫链，并对它们的应用进行了重点介绍。文中首先根据复合泊松过程理论，构造出股价波动过程模型，描述了股票价格过程，然后结合期权定价理论推导出期权定价公式，最后结合实际案例来分析，证明了模型的合理性和可用性，为证券投资者在股票价格分析上提供了帮助。另一方面考虑到教育教学质量问题在我们现实生活中有重要作用，并且研究发现高校教师教学过程存在着显著的马尔可夫性，所以根据马尔可夫链的相关性质，构造出一种可持续发展的高校教师教学质量评价的动态模型，进一步对模型进行了分析，最后给出了某高校的具体实例进行模型验证，表明模型的应用性和科学性，为高校的教学教育质量综合评价提供了一定的帮助。

关键词：泊松过程；马尔可夫链；期权定价；教师教学质量
 
Introduction and application of several typical random processes

Abstract：The theory system of random process is very common in our life application. This paper mainly introduces two typical random processes: Poisson process and Markov chain, and introduces their applications. In this paper, based on the compound Poisson process theory, the model of the stock price fluctuation process is constructed, the stock price process is described, then the option pricing formula is derived from the option pricing theory. Finally, the rationality and availability of the model are proved by the actual case, which provides the certificate investors to provide the stock price analysis. Help. On the other hand, the quality of education and teaching is considered to have an important role in our real life, and the study found that there is a significant Markov process in the teaching process of college teachers, so a dynamic model of the evaluation of teaching quality for sustainable development of college teachers is constructed according to the related nature of Markov chain. The model is analyzed by step. Finally, the concrete example of a university is given to verify the model, which shows the applicability and scientificity of the model, which provides a certain help for the comprehensive evaluation of the quality of teaching and education in Colleges and universities.

Key words:Poisson process; Markov chain,;Option pricing; Teaching quality of teachers

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