摘要
圣彼得堡概率学派对大数定理的研究奠定了概率论的理论基础。切比雪夫(Pierre-Simon marquisde Laplace,1749-1827)的研究动机就是试图应用不等式来精密估计确定试验下极限定理所产生的偏差,于1845年首先严格证明了伯努利大数定理,并于1866年给出一般情形下的切比雪夫大数定理。马尔可夫不满足于切比雪夫所要求随机变量方差值一致有界之条件,进一步改进了切比雪夫的结果,于1907年得到马尔可夫大数定理。圣彼得堡概率学派对大数定理理论的相关研究为概率论发展带来了生机,拓展了概率论的研究领域和发展空间,提升了俄罗斯乃至世界的概率论研究水平。
The St. Petersburg Probability School’s theorem of large numbers laid the foundation for probability theory. Chebyshev tried to use inequalities to estimate exactly the possible deviations from limit theorem under certain amount of tests. Chebyshev gave the first rigorous proof about Bernoulli’s theorem of large numbers in 1845, and gave the Chebyshev’s theorem of large numbers in 1866, which can be applied to general situations. Markov reduced the boundary conditions of the random variable, and provided the Markov’s theorem of large numbers in 1907.The probability school inherited and developed the essence of classical probability theory, and put forward a series of effective methods and led the probability research to a new era.
出处
《自然辩证法通讯》
CSSCI
北大核心
2013年第1期50-56,127,共7页
Journal of Dialectics of Nature
基金
教育部人文社会科学规划基金项目"圣彼得堡概率学派的思想研究"(10YJA720035)
关键词
圣彼得堡概率学派概率论随机变量
大数定理
The St. Petersburg Probability School
Probability theory
Random variable
Theorem of large numbers
