Self-similar diffusions on a class of infinitely ramified fractals

Hirofumi OSADA

doi:10.2969/jmsj/04740591

Hirofumi OSADA

著者情報

ジャーナルフリー

1995 年 47 巻 4 号 p. 591-616

DOI https://doi.org/10.2969/jmsj/04740591

詳細

Published: 1995 Received: 1993/02/25 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. T. Barlow and R. F. Bass, The construction of Brownian motion on the Sierpinski carpet, Ann. Inst. H. Poincaré, 25 (1989), 225-257.
2) M. T. Barlow and R. F. Bass, Local time for Brownian motion on the Sirpinski carpet, Probab. Theory Related Fields, 85 (1990), 91-104.
3) M. T. Barlow and R. F. Bass, On the resistence of the Sierpinski carpet, Proc. Roy. Soc. London Ser. A, 431 (1990), 354-360.
4) M. T. Barlow and R. F. Bass, Transition densities for Brownian motion on the Sierpinski carpet, Probab. Theory Related Fields, 91 (1992), 307-330.
5) M. T. Barlow, R. F. Bass and J. D. Sherwood, Resistence and spectral dimension of Sierpinski carpets, J. Phys. A, 23 (1990), L253-L258.
6) M. T. Barlow and E. A. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Related Fields, 79 (1988), 542-624.
7) S. Goldstein, Random walks and diffusions on fractals, In: Percolation theory and ergodic theory of infinite particle systems, (ed. H. Kesten), IMA Math. Appl., vol. 8, Springer, New York, 1987, pp. 121-129.
8) K. Hattori, T. Hattori and H. Watanabe, Gaussian field theories on general networks and the spectral dimensions, Progr. Theoret. Phys. Suppl., 92 (1987), 108-143.
9) J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
10) J. Kigami, Harmonic calculus on p.c.f. self-similar sets, to appear in Trans. Amer. Math. Soc., Vol. 335, Num. 2 (1993), 721-755.
11) T. Kumagai, Construction and some properties of a class of non-symmetric diffusion process on the Sierpinski gaskets, In: Asymptotic Problems in Probability Theory: stochastic models and diffusions on fractals, (eds. K. D. Elworthy and N. Ikeda), Pitman, 1993, pp. 219-247.
12) S. Kusuoka, A diffusion Process on a fractal, Probabilistic Methods of Mathematical Physics, Proc. of Taniguchi Symp., Katata and Kyoto 1985, (eds. K. Ito and N. Ikeda), Kinokuniya, Tokyo, 1987, pp. 251-274.
13) S. Kusuoka and X. Y. Zhou, Dirichlet forms of fractals: Poincaré constant and resistence, Probab. Theory Related Fields, 93 (1992), 169-196.
14) T. Lindstrøm, Brownian motion on nested Fractals, Mem. Amer. Math. Soc., 420 (1990).
15) H. Osada, Cell fractals and equations of hitting probabilities, In: Probability theory and mathematical statistics, (eds. A. Shiryaev, V. Korolyuk, S. Watanabe and M. Fukushima), World Scientific Publishing, 1992, pp. 248-258.
16) E. Seneta, Non-negative matrices and Markov chains, Springer-Verlag, 1980.

Right : [1] M. T. Barlow and R. F. Bass, The construction of Brownian motion on the Sierpinski carpet, Ann. Inst. H. Poincaré, 25 (1989), 225-257.
[2] M. T. Barlow and R. F. Bass, Local time for Brownian motion on the Sirpinski carpet, Probab. Theory Related Fields, 85 (1990), 91-104.
[3] M. T. Barlow and R. F. Bass, On the resistence of the Sierpinski carpet, Proc. Roy. Soc. London Ser. A, 431 (1990), 354-360.
[4] M. T. Barlow and R. F. Bass, Transition densities for Brownian motion on the Sierpinski carpet, Probab. Theory Related Fields, 91 (1992), 307-330.
[5] M. T. Barlow, R. F. Bass and J. D. Sherwood, Resistence and spectral dimension of Sierpinski carpets, J. Phys. A, 23 (1990), L253-L258.
[6] M. T. Barlow and E. A. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Related Fields, 79 (1988), 542-624.
[7] S. Goldstein, Random walks and diffusions on fractals, In: Percolation theory and ergodic theory of infinite particle systems, (ed. H. Kesten), IMA Math. Appl., vol. 8, Springer, New York, 1987, pp. 121-129.
[8] K. Hattori, T. Hattori and H. Watanabe, Gaussian field theories on general networks and the spectral dimensions, Progr. Theoret. Phys. Suppl., 92 (1987), 108-143.
[9] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
[10] J. Kigami, Harmonic calculus on p. c. f. self-similar sets, to appear in Trans. Amer. Math. Soc., Vol. 335, Num. 2 (1993), 721-755.
[11] T. Kumagai, Construction and some properties of a class of non-symmetric diffusion process on the Sierpinski gaskets, In: Asymptotic Problems in Probability Theory: stochastic models and diffusions on fractals, (eds. K. D. Elworthy and N. Ikeda), Pitman, 1993, pp. 219-247.
[12] S. Kusuoka, A diffusion Process on a fractal, Probabilistic Methods of Mathematical Physics, Proc. of Taniguchi Symp., Katata and Kyoto 1985, (eds. K. Ito and N. Ikeda), Kinokuniya, Tokyo, 1987, pp. 251-274.
[13] S. Kusuoka and X. Y. Zhou, Dirichlet forms of fractals: Poincaré constant and resistence, Probab. Theory Related Fields, 93 (1992), 169-196.
[14] T. Lindstrøm, Brownian motion on nested fractals, Mem. Amer. Math. Soc., 420 (1990).
[15] H. Osada, Cell fractals and equations of hitting probabilities, In: Probability theory and mathematical statistics, (eds. A. Shiryaev, V. Korolyuk, S. Watanabe and M. Fukushima), World Scientific Publishing, 1992, pp. 248-258.
[16] E. Seneta, Non-negative matrices and Markov chains, Springer-Verlag, 1980.

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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