概率统计由线性到非线性的发展  

The Development of Probability and Statistics——from Linear to Nonlinear Case

作　　者：陈增敬[1] 冯新伟 CHEN Zengjing;FENG Xinwei(School of Mathematics,Shandong University,Jinan,Shandong 250100,China;Zhongtai Securities Institute for Financial Studies,Shandong University,Jinan,Shandong 250100,China)

机构地区：[1]山东大学数学学院,山东济南250100 [2]山东大学中泰证券金融研究院,山东济南250100

出　　处：《数学建模及其应用》2023年第2期125-134,共10页Mathematical Modeling and Its Applications

摘　　要：概率统计是研究不确定现象的数学学科,它的本质就是从不确定现象中找确定的统计规律.三百多年以来,概率统计不仅推动了数学由确定性数学到随机数学的发展,也为经济、金融、物理、化学和生物等学科的发展提供了有效的计量工具和方法.随着大数据、人工智能和经济金融的飞速发展,现代概率统计已不能满足经济和科技发展的需要,发展和创新概率统计,为大数据、人工智能和经济金融提供理论基础和计算方法已是数学家攻克的重点热点问题.为了满足概率统计爱好者的需要,本文简单地介绍了概率统计发展的过程、对科学发展的作用、面临的问题和目前正在开展的新的研究方向,从另一个侧面介绍一下概率统计前世与后生.Probability and statistics are mathematical subjects that study uncertain phenomena,and the essence is to find the statistical laws from uncertain phenomena.For more than 300 years,probability and statistics not only promote the development of mathematics from deterministic to stochastic mathematics,but also provide effective tools and methods for the development of economics,finance,physics,chemistry,biology and other disciplines.With the rapid development of big data,artificial intelligence,economy and finance,classical probability and statistics can no longer meet the needs of economic and technological development.Therefore,innovating probability and statistics to provide theoretical basis for big data,artificial intelligence,economy and finance has become a key issue for mathematics.In this paper,we briefly introduce the development of classical probability and statistics,the roles in scientific development,the problems that we face and the future research directions.

关 键 词：概率论 极限定理 金融革命 非线性期望 非线性正态分布 

分 类 号：O29[理学—应用数学]