## 更新过程交替更新过程模拟实现及其性质的数值分析

Title    Numerical analysis and simulation about the character of the renewal process and alternative renewal process
Abstract
In real life, stochasticprocess has been widely used in many fields such as weather forecasting, statistical physics, astrophysics, operational decision-making, economic mathematics, safety science, population theory, reliability, and computer science, which have frequently used the stochastic process theory to establish the mathematical model. Therefore, we need to understand the stochastic process better and deeper 源`自<六:维;论-文>网/www.lwfree.cn
As the theory and application of the renewal process occupy an important position in stochasticprocess，in this paper, renewal process is mainly discussed. First, we give the classification of stochastic processes and its application background, then give the character and statistical analysis of the Poisson process, the method for generating random numbers which follow the exponential distribution, and gain the simulation of the sample orbits. Furthermore, we introduce the renewal process. Finally, we analyze the alternative renewal process, and also get the sample orbits by MATLAB. Through this paper, we can learn more about the theory and application of renewal process.
Keywords  stochastic process  Poisson process  random numbers  renewal process  simulation

1 绪论    1
1.1 课题的研究背景及意义    1
1.2 国内外研究现状    1
2 随机过程的基本概念    1
2.1 随机过程的概念与举例    2
2.2随机过程的数字特征及有限维分布函数族    2
2.3随机过程的分类    2
3 泊松过程及更新过程    4
3.1 泊松过程的定义    4
3.2 泊松过程的性质    6
3.3 泊松过程的统计分析    6
3.4  更新过程    7
4更新过程的模拟、检验及参数估计    10
4.1更新时间间隔服从指数分布的更新过程的模拟、检验及参数估计    10
4.2更新时间间隔服从对数正态分布的更新过程模拟、检验与参数估计    22
4.3  更新时间间隔服从均匀分布的更新过程模拟、检验与参数估计    27 源`自<六:维;论-文>网/www.lwfree.cn
4.4 交替更新过程的模拟、检验与参数估计    33

1 绪论
1.1 课题的研究背景及意义

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