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Volumn 30, Issue 5, 1997, Pages 605-673

Existence and uniqueness of diffusions on finitely ramified self-similar fractals

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EID: 0031536927     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(97)89934-X     Document Type: Article
Times cited : (118)

References (28)
  • 2
    • 0001035130 scopus 로고
    • Construction of the Brownian motion on the Sierpinski carpet
    • [2] M. T. BARLOW and R. F. BASS, Construction of the Brownian motion on the Sierpinski carpet, (Ann. Inst. Henri Poincaré, Vol. 25, 1989, pp. 225-257).
    • (1989) Ann. Inst. Henri Poincaré , vol.25 , pp. 225-257
    • Barlow, M.T.1    Bass, R.F.2
  • 3
    • 0000835875 scopus 로고
    • Brownian motion on the Sierpinski gasket
    • [3] M. T. BARLOW and E. A. PERKINS, Brownian motion on the Sierpinski gasket (Prob. Th. Rel. Fields, Vol. 79, 1988, pp. 543-623).
    • (1988) Prob. Th. Rel. Fields , vol.79 , pp. 543-623
    • Barlow, M.T.1    Perkins, E.A.2
  • 4
    • 0002936306 scopus 로고
    • Asymptotic behaviour of non-linear contraction semigroups
    • [4] C. M. DAFERMOS and M. SLEMROD, Asymptotic behaviour of non-linear contraction semigroups (J. Functional Analysis, Vol. 13, 1973, pp. 97-106).
    • (1973) J. Functional Analysis , vol.13 , pp. 97-106
    • Dafermos, C.M.1    Slemrod, M.2
  • 7
    • 0003523792 scopus 로고
    • Dirichlet forms and symetric Markov processes
    • Walter de Gruyter, Berlin, New-york
    • [7] M. FUKUSHIMA, Y. OSHIMA and M. TAKEDA, Dirichlet forms and symetric Markov processes (de Gruyter Stud. Math., Vol. 19, Walter de Gruyter, Berlin, New-york, 1994).
    • (1994) De Gruyter Stud. Math. , vol.19
    • Fukushima, M.1    Oshima, Y.2    Takeda, M.3
  • 8
    • 0000648822 scopus 로고
    • Dirichlet forms, diffusion processes and spectral dimensions for nested fractals
    • Ideas and Methods in Mathematical analysis, Stochastics and Applications (S. Albevario et al., eds.), Cambridge Univ. Press, Cambridge
    • [8] M. FUKUSHIMA, Dirichlet forms, diffusion processes and spectral dimensions for nested fractals, in: Ideas and Methods in Mathematical analysis, Stochastics and Applications (Proc. Conf. in Memory of Hoegh-Krohn, Vol. 1 (S. Albevario et al., eds.), Cambridge Univ. Press, Cambridge, 1993, pp. 151-161).
    • (1993) Proc. Conf. in Memory of Hoegh-Krohn , vol.1 , pp. 151-161
    • Fukushima, M.1
  • 9
    • 0001582569 scopus 로고
    • Random walks and diffusions on fractals
    • (H. Kesten, ed.), Springer-Verlag, New York
    • [9] S. GOLDSTEIN, Random walks and diffusions on fractals, in: IMA Math Appl., Vol. 8 (H. Kesten, ed.), Springer-Verlag, New York, 1987, pp. 121-129).
    • (1987) IMA Math Appl. , vol.8 , pp. 121-129
    • Goldstein, S.1
  • 10
    • 0001698331 scopus 로고
    • Gaussian field theories on general networks and the spectral dimensions
    • [10] K. HATTORI, T. HATTORI, H. WATANABE, Gaussian field theories on general networks and the spectral dimensions (Progress of Theoritical Physics, Supplement No 92, 1987).
    • (1987) Progress of Theoritical Physics , Issue.SUPPL. NO 92
    • Hattori, K.1    Hattori, T.2    Watanabe, H.3
  • 11
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • [11] J. E. HUTCHINSON, Fractals and self-similarity (Indiana Univ. Math. J., Vol. 30, 1981, pp. 713-747).
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 713-747
    • Hutchinson, J.E.1
  • 12
    • 84924341601 scopus 로고
    • Harmonic calculus on p.c.f. self-similar sets
    • [12] J. KIGAMI, Harmonic calculus on p.c.f. self-similar sets, (Trans. Am. Math. Soc., Vol. 335, 1993, pp. 721-755) .
    • (1993) Trans. Am. Math. Soc. , vol.335 , pp. 721-755
    • Kigami, J.1
  • 13
    • 0002343091 scopus 로고
    • Harmonic calculus on limits of networks and its application to dendrites
    • February 15
    • [13] J. KIGAMI, Harmonic calculus on limits of networks and its application to dendrites (Journal of Functional Analysis, Vol. 128, No. 1, February 15, 1995).
    • (1995) Journal of Functional Analysis , vol.128 , Issue.1
    • Kigami, J.1
  • 14
    • 0000430442 scopus 로고
    • Regularity, closedness, and spectral dimension of the Dirichlet forms on p.c.f. self-similar sets
    • [14] T. KUMAGAI , Regularity, closedness, and spectral dimension of the Dirichlet forms on p.c.f. self-similar sets (J. Math. Kyoto Univ., Vol. 33, 1993, pp. 765-786).
    • (1993) J. Math. Kyoto Univ. , vol.33 , pp. 765-786
    • Kumagai, T.1
  • 15
    • 0002070668 scopus 로고
    • A diffusion process on a fractal
    • Probabilistic Methods in Mathematical Physics (K. Ito and N. Ikeda, eds.) Kinokuniya, Tokyo
    • [15] S. KUSUOKA, A diffusion process on a fractal, in: (Probabilistic Methods in Mathematical Physics (Proc. of Taniguchi Intern. Symp. (K. Ito and N. Ikeda, eds.) Kinokuniya, Tokyo, 1987, pp. 251-274).
    • (1987) Proc. of Taniguchi Intern. Symp. , pp. 251-274
    • Kusuoka, S.1
  • 17
    • 0001313307 scopus 로고
    • Analysis on fractals, Laplacians on self-similar sets, non-commutative geometry and spectral dimensions
    • [17] M. L. LAPIDUS, Analysis on fractals, Laplacians on self-similar sets, non-commutative geometry and spectral dimensions (Topological Methods in Nonlinear Analysis, Vol. 4, No 1, 1994 i, pp. 137-195).
    • (1994) Topological Methods in Nonlinear Analysis , vol.4 , Issue.1 , pp. 137-195
    • Lapidus, M.L.1
  • 18
    • 0003126003 scopus 로고
    • Mesures associées à une forme de Dirichlet. Applications
    • [18] Y. LE JAN, Mesures associées à une forme de Dirichlet. Applications (Bull. Soc. Math. de France, Vol. 106, 1978, pp. 61-112).
    • (1978) Bull. Soc. Math. de France , vol.106 , pp. 61-112
    • Le Jan, Y.1
  • 19
    • 0000311503 scopus 로고
    • Brownian motion on nested fractals
    • [19] T. LINDSTRØM, , Brownian motion on nested fractals (Mem. Amer. Math. Soc., Vol. 420, 1990).
    • (1990) Mem. Amer. Math. Soc. , vol.420
    • LindstrØm, T.1
  • 20
    • 0000921622 scopus 로고
    • How many diffusions exist on the Viscek snowflake
    • [20] V. METZ, How many diffusions exist on the Viscek snowflake (Acta Applicandae Mathematicae, Vol. 32, 1993, pp. 227-241) .
    • (1993) Acta Applicandae Mathematicae , vol.32 , pp. 227-241
    • Metz, V.1
  • 21
    • 0010780407 scopus 로고
    • Hilbert's projective metric on cones of Dirichlet forms
    • [21] V. METZ, Hilbert's Projective metric on cones of Dirichlet forms (Journal of Functional Analysis, Vol 127, No 2, 1995).
    • (1995) Journal of Functional Analysis , vol.127 , Issue.2
    • Metz, V.1
  • 22
    • 0039771567 scopus 로고
    • Additive functions of intervals and Haussdorf measure
    • [22] MORAN, Additive functions of intervals and Haussdorf measure (Math. Proc., Cambridge Philos. Soc., Vol. 42, 1946, pp. 15-23).
    • (1946) Math. Proc., Cambridge Philos. Soc. , vol.42 , pp. 15-23
    • Moran1
  • 23
    • 0001338184 scopus 로고
    • Hilbert's protective metric and iterated nonlinear maps
    • Amer. Math. Soc. Providence
    • [23] R.D. NUSSBAUM, Hilbert's Protective Metric and Iterated Nonlinear Maps (Mem. Am. Math. Soc., Vol 75, No 391, Amer. Math. Soc. Providence, 1988).
    • (1988) Mem. Am. Math. Soc. , vol.75 , Issue.391
    • Nussbaum, R.D.1
  • 24
    • 0010851125 scopus 로고
    • The structure of w-limit sets of non-expansive maps
    • [24] S. ROEHRIG and R. SINE, The structure of w-limit sets of non-expansive maps (Proc. Amer. Math. Soc., Vol. 81, 1981, pp. 398-400).
    • (1981) Proc. Amer. Math. Soc. , vol.81 , pp. 398-400
    • Roehrig, S.1    Sine, R.2
  • 26
    • 0001181146 scopus 로고
    • Existence et unicité de la diffusion sur un espace fractal
    • [26] C. SABOT, Existence et unicité de la diffusion sur un espace fractal (C. R. Acad. Sci. Paris, T. 321, Séries I, pp. 1053-1059, 1995).
    • (1995) C. R. Acad. Sci. Paris , vol.321 , Issue.I , pp. 1053-1059
    • Sabot, C.1
  • 28
    • 0000245433 scopus 로고
    • Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donnée
    • [28] W. SIERPINSKI , Sur une courbe Cantorienne qui contient une image biunivoque et continue de toute courbe donnée (C. R. Acad. Sci. Paris, T. 162, 1916, pp. 629-632).
    • (1916) C. R. Acad. Sci. Paris , vol.162 , pp. 629-632
    • Sierpinski, W.1


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