no. 3
The construction of brownian motion on the Sierpinski carpet
Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) no. 3, pp. 225-257. 
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     title = {The construction of brownian motion on the {Sierpinski} carpet},
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     pages = {225--257},
     publisher = {Gauthier-Villars},
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     number = {3},
     year = {1989},
     mrnumber = {1023950},
     zbl = {0691.60070},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1989__25_3_225_0/}
}
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Barlow, Martin T.; Bass, Richard F. The construction of brownian motion on the Sierpinski carpet. Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) no. 3, pp. 225-257. http://www.numdam.org/item/AIHPB_1989__25_3_225_0/

[1] M.T. Barlow and E. Perkins, Brownian Motion on the Sierpinski Gasket, Prob. Th. and related Fields, Vol. 79, 1988, pp. 543-623. | MR | Zbl

[2] R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR | Zbl

[3] R.M. Blumenthal, R.K. Getoor and H.P. Mckean Jr., Markov Processes with Identical Hitting Distributions, Ill. J. Math., Vol. 6, 1962, pp. 402-420, Vol. 7, 1963, pp. 540-542. | MR | Zbl

[4] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel: Théorie des Martingales, Hermann, Paris, 1980. | MR | Zbl

[5] S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986. | MR | Zbl

[6] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland/Kodansha, Tokyo, 1980. | MR | Zbl

[7] S. Goldstein, Random Walks and Diffusions on Fractals, I.M.A. vol. in Math & Applic., Percolation Theory and Ergodic Theory of Infinite Particle Systems, H. KESTEN Ed., 121-129. Springer, New York, 1987. | Zbl

[8] H. Kesten, Subdiffusive Behavior of Random Walk on a Random Cluster, Ann. Inst. H.-Poincaré, Vol. 22, 1986, pp. 425-487. | Numdam | MR | Zbl

[9] N.V. Krylov and M.V. Safonov, An Estimate of the Probability that a Diffusion Process hits a Set of Positive Measure, Soviet Math. Doklady, Vol. 20, 1979, pp. 253- 255. | Zbl

[10] S. Kusuoka, A Diffusion Process on a Fractal, in Probabilistic Methods in Mathematical Physics, Taniguchi Symp., Katata, 1985, K. ITO, N. IKEDA Ed., pp. 251-274, Kinokuniya-North Holland, Amsterdam, 1987. | MR | Zbl

[11] B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982. | MR | Zbl

[12] J. Moser, On Harnack's Theorem for Elliptic Differential Equations, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 577-591. | MR | Zbl

[13] S.C. Port and C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, New York, 1978. | MR | Zbl

[14] R. Rammal and G. Toulouse, Random Walks on Fractal Structures and Percolation Clusters, J. Physique lettres, Vol. 44, 1983, pp. L13-L22.

[15] 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. | JFM

[16] R. Wittmann, Natural Densities for Markov Transition Probabilities, Prob. Th. and related Fields, Vol. 73, 1986, pp. 1-10. | MR | Zbl