The construction of brownian motion on the Sierpinski carpet

Martin T. Barlow; Richard F. Bass

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 3, page 225-257
  • ISSN: 0246-0203

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Barlow, Martin T., and Bass, Richard F.. "The construction of brownian motion on the Sierpinski carpet." Annales de l'I.H.P. Probabilités et statistiques 25.3 (1989): 225-257. <http://eudml.org/doc/77350>.

@article{Barlow1989,
author = {Barlow, Martin T., Bass, Richard F.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Brownian motion; Sierpinski carpet; finitely ramified fractal},
language = {eng},
number = {3},
pages = {225-257},
publisher = {Gauthier-Villars},
title = {The construction of brownian motion on the Sierpinski carpet},
url = {http://eudml.org/doc/77350},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Barlow, Martin T.
AU - Bass, Richard F.
TI - The construction of brownian motion on the Sierpinski carpet
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 3
SP - 225
EP - 257
LA - eng
KW - Brownian motion; Sierpinski carpet; finitely ramified fractal
UR - http://eudml.org/doc/77350
ER -

References

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  2. [2] R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. Zbl0169.49204MR264757
  3. [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. Zbl0133.40903MR142157
  4. [4] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel: Théorie des Martingales, Hermann, Paris, 1980. Zbl0464.60001MR566768
  5. [5] S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986. Zbl0592.60049MR838085
  6. [6] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland/Kodansha, Tokyo, 1980. Zbl0422.31007MR569058
  7. [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. Zbl0621.60073
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  10. [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. Zbl0645.60081MR933827
  11. [11] B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982. Zbl0504.28001MR665254
  12. [12] J. Moser, On Harnack's Theorem for Elliptic Differential Equations, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 577-591. Zbl0111.09302MR159138
  13. [13] S.C. Port and C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, New York, 1978. Zbl0413.60067MR492329
  14. [14] R. Rammal and G. Toulouse, Random Walks on Fractal Structures and Percolation Clusters, J. Physique lettres, Vol. 44, 1983, pp. L13-L22. 
  15. [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. Zbl46.0295.02JFM46.0295.02
  16. [16] R. Wittmann, Natural Densities for Markov Transition Probabilities, Prob. Th. and related Fields, Vol. 73, 1986, pp. 1-10. Zbl0581.60057MR849062

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