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The Splendors and Miseries of MartingalesMartingales in Japan

The Splendors and Miseries of Martingales: Martingales in Japan [Japanese mathematicians did not contribute directly to martingale theory before 1960, but many later contributions were based on the stochastic calculus that Kiyosi Itô first introduced in 1942. Itô’s collaboration with Henry McKean on the pathwise construction of diffusions attracted wide interest from students in Japan. Subsequent Japanese contributions in the 1960s included adaptations of results on Markov processes to martingales, such as Itô and Watanabe’s multiplicative analog of the Doob–Meyer decomposition, which involved the introduction of local martingales, contributions to stochastic integration for square-integrable martingales and semimartingales, and contributions to the representation of martingales. Japanese contributions after 1970 included Itô’s reformulation of the stochastic calculus in term of stochastic differentials, Itô’s circle operation, the Itô–Tanaka formula, and the Fukushima decomposition.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesMartingales in Japan

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn
Watanabe, Shinzo
The Splendors and Miseries of Martingales — Oct 18, 2022
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References (1)

  • MHA Davis (1974)

    958

    The Annals of Probability, 2

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
203 –214
DOI
10.1007/978-3-031-05988-9_9
Publisher site
See Chapter on Publisher Site

Abstract

[Japanese mathematicians did not contribute directly to martingale theory before 1960, but many later contributions were based on the stochastic calculus that Kiyosi Itô first introduced in 1942. Itô’s collaboration with Henry McKean on the pathwise construction of diffusions attracted wide interest from students in Japan. Subsequent Japanese contributions in the 1960s included adaptations of results on Markov processes to martingales, such as Itô and Watanabe’s multiplicative analog of the Doob–Meyer decomposition, which involved the introduction of local martingales, contributions to stochastic integration for square-integrable martingales and semimartingales, and contributions to the representation of martingales. Japanese contributions after 1970 included Itô’s reformulation of the stochastic calculus in term of stochastic differentials, Itô’s circle operation, the Itô–Tanaka formula, and the Fukushima decomposition.]

Published: Oct 18, 2022

Keywords: Additive functional; Hunt process; Itô’s circle operation; Itô–Tanaka formula; Martingale; Markov process; Multiplicative decomposition; Sample function; Semimartingale; Watanabe decomposition; Fukushima decomposition

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