P. L. Chebyshev的概率新思想溯源

A Research on P. L. Chebyshev's Thoughts in Probability and Its Mathematical Background and Motivation

中文关键词:  切贝舍夫  大数定律  概率  数学期望  圣彼得堡.

英文关键词:P.L. Chebyshev  law of large numbers  probability  expectation  St. Petersburg.

中文摘要:

      切贝舍夫是俄国十九世纪最伟大的数学家之一,他第一个主张概率论的极限定理应该严格的证明,并尽可能精确地确定偏离极限的估计量,这在方法论上引起了很大变化.其创立的切贝舍夫不等式和切贝舍夫大数定律是概率论极限理论的基础,从而使概率论成为严密数学分支.切贝舍夫的概率思想是在一定数学文化背景产生的,尤其是法国数学文化对其发展的形成有着深刻影响.

英文摘要:

      P. L. Chebyshev was the greatest mathematician in Russian Empire in 18th century. It was him that advocated that the limit theorem of probability should be proved strictly, and the deviation from the limit value should be estimit as accurately as possibly. These caused great changes in methodology. Chebyshev's Inequality and Law of Large Numbers are the foundational work on the limit theory of probability. Its publication symbolizes the rigorize of the theory of probability as a branch of mathematics. This paper analyses P.L.Chebyshev's novel thoughts on probability, and concentrate on the earlier period that culminates with Chebyshev, and specifically on the mathematical background and motivation for his activity in probability.