Stochastic Process - Conflict

…He has been affiliated with the University of Illinois since 1935, and became a professor in 1945. He conducted systematic research on the foundations of stochastic processes, and was particularly notable for his work on the theory of separable transformations and martingales, the results of which were included in his book Stochastic Processes, published in 1953. Martingales are important stochastic processes that can be considered a model for fair gambling, and P. Levi and others began researching them. Doob also introduced the concept of submartingales, creating a beautiful theory that could be called the probabilistic version of the theory of (sub)harmonic functions in analysis. …

*Some of the terminology explanations that mention "stochastic process" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…1935年以来イリノイ大学に所属し，45年教授となる。確率過程論の基礎に関する系統的研究を行い，とくに可分変形の理論とマルチンゲールの理論は著しく，その成果は53年刊行の著書《確率過程》に収められている。マルチンゲールは公平なかけ事のモデルと考えられる重要な確率過程であり，P.レビらが研究を始めたが，ドゥーブはそれとともに劣マルチンゲールという概念も導入し，解析学における(劣)調和関数論の確率論版ともいうべき美しい理論を作った。…

※「《確率過程》」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報