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Local times for Brownian motion on the Sierpinski carpet
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  • Published: March 1990

Local times for Brownian motion on the Sierpinski carpet

  • Martin T. Barlow1 &
  • Richard F. Bass2 

Probability Theory and Related Fields volume 85, pages 91–104 (1990)Cite this article

  • 158 Accesses

  • 23 Citations

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Summary

Jointly continuous local times are constructed for Brownian motion on the Sierpinski carpet. A consequence is that the Brownian motion hits points. The method used is to analyze a sequence of eigenvalue problems.

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References

  1. Barlow, M.T., Bass, R.F.: The construction of Brownian motion on the Sierpinski carpet. Ann. l'IHP,25, 225–257 (1989)

    Google Scholar 

  2. Barlow, M.T., Bass, R.F.: (in preparation)

  3. Barlow, M.T., Perkins, E.A.: Brownian motion on the Sierpinski gasket. Probab. Th. Rel. Fields,79, 543–623 (1988)

    Google Scholar 

  4. Ben-Avraham, D., Havlin, S.: Exact fractals with adjustable fractal and fracton dimensionalities. J. Phys. A.16, L559-L563 (1983)

    Google Scholar 

  5. Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York London: Academic Press 1968

    Google Scholar 

  6. Courant, R., Hilbert, D.: Methods of mathematical physics, vol. 1. New York: Interscience 1953

    Google Scholar 

  7. Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel: théorie des martingales. Paris: Hermann 1980

    Google Scholar 

  8. Doyle, P.G., Snell, J.L.: Random walks and electrical networks. Washington DC: Math. Assoc. Am. 1984

    Google Scholar 

  9. Durrett, R.: Brownian motion and martingales in analysis. Belmont CA.: Wadsworth 1984

    Google Scholar 

  10. Gilbarg, D., Trudinger, N.S.: Elliptic partic partial differential equations of second order. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  11. Goldstein, S.: Random walks and diffusions on fractals, In: Kesten, H. (ed.) Percolation theory and ergodic theory of infinite particle systems. (IMA Vol. Math. Appl. vol. 8, pp. 121–129) Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  12. Havlin, S., ben-Avraham, D.: Diffusion in disordered media. Adv. Phys.36, 695–798 (1987)

    Google Scholar 

  13. Kusuoka, S.: A diffusion process on a fractal, In: Ito, K., Ikeda, N. (eds.) Probabilistic methods in mathematical physics, Taniguchi Symp., Katata 1985, pp. 251–274, Boston: Academic Press, 1987

    Google Scholar 

  14. Lindstrom, T.: Brownian motion on nested fractals, Mem. Am. Math. Soc. (to appear)

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Author information

Authors and Affiliations

  1. Statistical Laboratory, 16 Mill Lane, CB2 1SB, Cambridge, UK

    Martin T. Barlow

  2. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    Richard F. Bass

Authors
  1. Martin T. Barlow
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  2. Richard F. Bass
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Additional information

Research partially supported by NSF grant DMS 87-01073

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Cite this article

Barlow, M.T., Bass, R.F. Local times for Brownian motion on the Sierpinski carpet. Probab. Th. Rel. Fields 85, 91–104 (1990). https://doi.org/10.1007/BF01377631

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  • Received: 24 February 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01377631

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Eigenvalue Problem
  • Local Time
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