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Local extinction of super-Brownian motion on Sierpinski gasket

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Abstract

The Brownian motion and super-Brownian motion on the Sierpinski gasket are studied. Firstly it is proved that the local extinction property is possessed by the super-Brownian motion on this fractal structure. This fact is also true even in the presence of catalyst. Secondly it is proved that the paths of the Brownian motion on the Sierpinski gasket are dense in some sense.

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References

  1. O’Shaughnessy, B., Procaccia, I., Diffusion on fractals,Physical Review A, 1985, 32: 3073.

    Article  MathSciNet  Google Scholar 

  2. Rammal, R., Touiouse, G., Random walks on fractal structures and percolation clusters,J. Physics Letters, 1983, 44: 13.

    Article  Google Scholar 

  3. Barlow, M. T., Bass, R. F., Transition densities for Brownian motion on the Sierpinski gasket,Probab. Th. Rel. Fields, 1992, 91: 307.

    Article  MATH  MathSciNet  Google Scholar 

  4. Hambly, B. M., Brownian motion on the homogeneous random fractal,Prob. Th. Rel. Fields, 1992, 94: 1.

    Article  MATH  MathSciNet  Google Scholar 

  5. Krebs, W. B., Hitting time bounds for Brownian motion on fractal,Proc.Am.Math. Soc. 1993, 118: 223.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kumagai, T., Estimation of transition densities for Brownian motion on nested fractals,Probab. Th. Rel. Fields, 1993, 96: 205.

    Article  MATH  MathSciNet  Google Scholar 

  7. Barlow, M. T., Perkins, E. A., Brownian motion on the Sierpinski gasket,Probab. Th. Rel. Fields, 1988, 79: 543.

    Article  MATH  MathSciNet  Google Scholar 

  8. Lindstr M, T., Brownian motion on nested fractals,USA: AMS,Mem. Am. Math. Soc., 1990, 420.

  9. Dawson, D. A., The critical measure diffusion process,Z. Wahrscheinlichkeitstheor Verw., 1977, 40: 125.

    Article  MATH  Google Scholar 

  10. Dawson, D. A., Fleischmann, K., A super-Brownian motion with a single point catalyst,Stock. Proc. Appl., 1994, 49: 3.

    Article  MATH  MathSciNet  Google Scholar 

  11. Dawson, D. A., Fleischmann, K., Critical branching in a highly fluctuating random medium,Probab. Th. Rel. Fields, 1991, 90: 241.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nankai University, 300071, Tianjin, China

    Junyi Guo

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  1. Junyi Guo
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Project supported by the National Natural Science Foundation of China.

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Guo, J. Local extinction of super-Brownian motion on Sierpinski gasket. Sci. China Ser. A-Math. 41, 260–266 (1998). https://doi.org/10.1007/BF02879044

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  • DOI: https://doi.org/10.1007/BF02879044

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