Basic properties of Brownian motion and a capacity on the Wiener space

Masatoshi FUKUSHIMA

doi:10.2969/jmsj/03610161

Masatoshi FUKUSHIMA

著者情報

ジャーナルフリー

1984 年 36 巻 1 号 p. 161-176

DOI https://doi.org/10.2969/jmsj/03610161

詳細

Published: 1984 Received: 1983/02/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Fukushima, Dirichlet forms and Markov processes, North Holland and Kodansha, 1980.
2) M. Fukushima, Capacitary maximal inequalities and an ergodic theorem, Proceedings of the 4-th USSR-Japan Symposium on Probability Theory and Mathematical Statistics, Lecture Notes in Math., 1021, Springer, 1983.
3) N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North Holland and Kodansha, 1981.
4) K. Ito and H. P. McKean, Diffusion processes and their sample paths, Springer, 1965.
5) S. Kakutani, On Brownian motion in n-space, Proc. Acad. Japan, 20 (1944), 648-652.
6) S. Kusuoka, Dirichlet forms and diffusion processes on Banach spaces, J. Fac. Sci. Univ. Tokyo Sect. IA, 29 (1982), 79-95.
7) H. P. McKean, Stochastic integrals, Academic Press, 1969.
8) P. A. Meyer, Note sur les processus d'Ornstein-Uhlenbeck (Appendice: Un resultat de D. Williams), Séminaire de Probabilités XVI 1980/81, Lecture Notes in Math., 920, Springer, 1982.
9) S. Orey and W. Pruitt, Sample functions of the N-parameter Wiener process, Ann. Probability, 1(1973), 138-163.
10) D. W. Stroock, The Malliavin calculus and its applications, Stochastic integrals, Lecture Notes in Math., 851, Springer, 1981.
11) M. Takeda, (r, p) -capacity on the Wiener space and properties of Brownian motion, to appear.
12) G. Zimmerman, Some sample function properties of the two-parameter Gaussian process, Ann. Math. Statist, 43 (1972), 1235-1246.

Right : [1] M. Fukushima, Dirichlet forms and Markov processes, North Holland and Kodansha, 1980.
[2] M. Fukushima, Capacitary maximal inequalities and an ergodic theorem, Proceedings of the 4-th USSR-Japan Symposium on Probability Theory and Mathematical Statistics, Lecture Notes in Math., 1021, Springer, 1983.
[3] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North Holland and Kodansha, 1981.
[4] K. Ito and H. P. McKean, Diffusion processes and their sample paths, Springer, 1965.
[5] S. Kakutani, On Brownian motion in n-space, Proc. Acad. Japan, 20 (1944), 648-652.
[6] S. Kusuoka, Dirichlet forms and diffusion processes on Banach spaces, J. Fac. Sci. Univ. Tokyo Sect. IA, 29 (1982), 79-95.
[7] H. P. McKean, Stochastic integrals, Academic Press, 1969.
[8] P. A. Meyer, Note sur les processus d'Ornstein-Uhlenbeck (Appendice: Un resultat de D. Williams), Séminaire de Probabilités XVI 1980/81, Lecture Notes in Math., 920, Springer, 1982.
[9] S. Orey and W. Pruitt, Sample functions of the N-parameter Wiener process, Ann. Probability, 1(1973), 138-163.
[10] D. W. Stroock, The Malliavin calculus and its applications, Stochastic integrals, Lecture Notes in Math., 851, Springer, 1981.
[11] M. Takeda, (r,p)-capacity on the Wiener space and properties of Brownian motion, to appear.
[12] G. Zimmerman, Some sample function properties of the two-parameter Gaussian process, Ann. Math. Statist, 43 (1972), 1235-1246.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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