Dube is an American mathematician. 1910/kloc-0 was born in Cincinnati on October 27th and died in Illinois on June 7th, 2004.
Du Bei graduated from Harvard University with a doctorate 1932. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and a professor at the University of Illinois.
Dube's main contribution is probability theory. He deeply studied the theory of random process, and obtained that any random process has separable corrections, and established the axiomatic structure of random function theory. He was the founder of martingale theory, although Levi and others published some works that gave birth to martingale theory as early as 1935, and in 1939, Will introduced the name "martingale". However, the systematic study of martingale and making it an important branch of stochastic process theory should be attributed to Dube. He also introduced the concept of semimartingale. In martingale theory, there are famous Dube Stop Theorem named after his surname, Dube-Meyer Martingale Decomposition Theorem and so on. Martingale theory further abstracted the study of stochastic process, which not only enriched the content of probability theory, but also provided other branches of mathematics such as harmonic analysis, complex variable function and potential theory.
The Markov process and Dube's strict treatment of orbit are systematically studied.
He also contributed to the theory of set-valued sets in algebraic functions. He also proved a special case of hopf's personal ergodic theorem. There are Dube theorem, Dube inequality, Dube convergence and so on in mathematics.