An operator-theoretical treatment of temporally homogeneous Markoff process

KÔSAKU YOSIDA

doi:10.2969/jmsj/00130244

KÔSAKU YOSIDA

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ジャーナルフリー

1949 年 1 巻 3 号 p. 244-253

DOI https://doi.org/10.2969/jmsj/00130244

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Published: 1949 Received: 1948/04/01 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/08/29 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : KOSAKU YOSIDA¹⁾
Right : KÔSAKU YOSIDA¹⁾

訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : 1) On the differentiability and the representation of the one-parameter semi-group of linear operators, the Journal of the Math. Soc. of Japan, 1 (1948).
2) We may obtain, similarly as (1.8), another representation of U_t: (1.8)' U_t x=lim_n→∞ (I-n^-1t A)^-n x.
3) P. Lévy: Théorie de l'addition des variables aléatoires, Paris (1937).
4) G. Birkhoff: Lattice Theory, New York (1940). S. Kakutani; Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Ann, of Math., 42 (1941).
5) Cf. N. Dunford and I. E. Segal: Semi-groups of operators and the Weierstrass theorem, Bullet. Amer. Math. Soc., 52 (1946).
6) A. A. Eddington: On a formula for correcting statistics for the effect of a known probable error of observations, Monthly Notice R. Astr. Soc., 73 (1914).
7) A. Kolmogoroff: Die analytische Methoden in der Wahrscheinlichkeitsrechnung, Math. Ann., 104 (1931).
8) A. Khintchine: Déduction nouvelle d'une formule de P. Lévy, Bullet, de l'université d'état à Moscow, Sect. A, 1 (1937).
9) Cf. W. Feller: Zur Theorie der stochastischen Prozesse, Math. Ann., 113 (1936). K. Itô: On stochastic processes (II), to appear in the Mem. of the Am. Math. Soc. Our method of integration may be extended to the Fokker-Planck's equation in homogeneous Riemannian spaces. For example, we may determine the “Brownian motion” on the surface of the sphere. The details will be published elsewhere. Here I express my hearty thanks to Dr. K. Itô for his friendly criticism during the preparation of the present note.

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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