Transition density estimates for brownian motion on scale irregular Sierpinski gaskets

 Access to full text

 Full (PDF)

1. [1] M.T. Barlow, Random walks, electrical resistance, and nested fractals, In: K. D. Elworthy, N. Ikeda (eds.) Asymptotic problems in probability theory: stochastic models and diffusion on fractals, Montreal, Pitman, 1993, pp. 131-157. Zbl0791.60097MR1354153
2. [2] M.T. Barlow and R.F. Bass, Construction of Brownian motion on the Sierpinski carpet, Ann. Inst. H. Poincaré, Vol. 25, 1989, pp. 225-257. Zbl0691.60070MR1023950
3. [3] M.T. Barlow and R.F. Bass, Transition densities for Brownian motion on the Sierpinski carpet, Prob. Theory Rel. Fields, Vol. 91, 1992, pp. 307-330. Zbl0739.60071MR1151799
4. [4] M.T. Barlow and E.A. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Rel. Fields, Vol. 79, 1988, pp. 543-624. Zbl0635.60090MR966175
5. [5] A. Beurling and J. Deny, Espaces de Dirichlet I, le cas élémentaire, Acta. Math., Vol. 99, 1958, pp. 203-224. Zbl0089.08106MR98924
6. [6] K.J. Falconer, Fractal Geometry, Wiley, Chichester, 1990. Zbl0689.28003MR1102677
7. [7] P.J. Fitzsimmons, B.M. Hambly and T. Kumagai, Transition density estimates for Brownain motion on affine nested fractals, Comm. Math. Phys., Vol. 165, 1994, pp. 595-620. Zbl0853.60062MR1301625
8. [8] M. Fukushima, Dirichlet forms, diffusion processes and spectral dimensions for nested fractals, In: Albeverio, Fenstad, Holden and Lindstrøm (eds.) Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, In Memory of R. Høegh-Krohn, vol. 1, Cambridge Univ. Press, 1992, pp. 151-161. Zbl0764.60081MR1190496
9. [9] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet forms and symmetric Markov processes, de Gruyter, Berlin, 1994. Zbl0838.31001MR1303354
10. [10] B.M. Hambly, Brownian motion on a homogeneous random fractal, Probab. Theory Rel. Fields, Vol. 94, 1992, pp. 1-38. Zbl0767.60075MR1189083
11. [11] B.M. Hambly, Brownian motion on a random recursive Sierpinski gasket, to appear Ann. Probab., 1997. Zbl0895.60081MR1457612
12. [12] S. Hutchinson, Self-similar sets, Indiana Univ. Math. J., Vol. 30, 1981, pp. 713-747. Zbl0598.28011
13. [13] J. Kigami, A harmonic calculus for p.c.f. self-similar sets, Trans. Am. Math. Soc., Vol. 335, 1993, pp. 721-755. Zbl0773.31009MR1076617
14. [14] J. Kigami, Harmonic calculus on limits of networks and its applications to dendrites, J. Funct. Anal., Vol. 128, 1995, pp. 48-86. Zbl0820.60060MR1317710
15. [15] T. Kumagai, Estimates of transition densities for Brownian motion on nested fractals, Proba. Theory Rel. Fields, Vol. 96, 1993, pp. 205-224. Zbl0792.60073MR1227032
16. [16] S. Kusuoka, Diffusion processes on nested fractals, In: Dobrushin, R. L., Kusuoka, S.: Statistical mechanics and fractals (Lect. Notes in Math.1569), Springer-Verlag, 1993. Zbl0787.60119
17. [17] S. Kusuoka and X.Y. Zhou, Dirichlet forms on fractals: Poincaré constant and resistance, Probab. Theory Relat. Fields, Vol. 93, 1992, pp. 169-196. Zbl0767.60076MR1176724
18. [18] T. Lindstrøm, Brownian motion on nested fractals, Memoirs Am. Math. Soc., Vol. 420, 1990. Zbl0688.60065MR988082
19. [19] R.D. Mauldin and S.C. Williams, Random recursive constructions: asymptotic geometric and topological properties, Trans. Am. Math. Soc., Vol. 295, 1990, pp. 325-346. Zbl0625.54047MR831202

1. Umberto Mosco, Analysis and Numerics of Some Fractal Boundary Value Problems