随机序贯分布和期望时间  

Distribution and Expectation of Stochastic Sequence

作　　者：卢金余 

机构地区：[1]江苏理工学院数理学院,江苏常州213001

出　　处：《江苏理工学院学报》2017年第4期32-39,共8页Journal of Jiangsu University of Technology

摘　　要：随机序贯分析广泛应用于自然科学、社会科学和工程技术,涉及概率推断、统计推断、秩序检验和预测等。研究与分析随机过程定性和定量数据,通过博弈论方法和随机序贯结构分析,证明和总结序贯出现期望时间结构和方差公式。建立几个随机模型,基于不确定数据或随机波动可转化为0~1时间序列,得出并求解更新方程、递推方程或差分方程,然后,由序贯期望时间结构得出序贯出现时间的生成函数和循环方程的一般规则。运用几种合适和有效的计算方法推导一些典型随机序贯出现时间的概率、分布及期望。分析了现代概率论的一些重要问题和典型应用例子。最后,定义并求出贝努利试验产生的连续序贯数的分布与矩等。This paper researches and analyzes qualitative and quantitative data of stochastic process. Random se- quential analysis is widely applied to natural science, social science and engineering technology, involving prohabilistic inference, statistical inference, rank order or sign test and prediction, etc. Through game theory and the structure analysis of random sequence, we demonstrated and summarized the structure of expectation and the for- mula of variance of stochastic sequences. Several stochastic models are established, with that uncertainty of data or random oscillator may be transferred into sign sequences. Renewal equation, recursive equation, and difference equation are inferred. Afterwards, the ordinary criteria of generating function and renewal equation are deduced via sequential time expectation structure. In several appropriate and effective calculating methods, representative random sequential emergence time probability, distribution and expectation are deviated.

关 键 词：随机序贯 概率生成函数 更新方程 递推方程 期望时间 概率分布 

分 类 号：O211[理学—概率论与数理统计]