Transition density estimates for brownian motion on scale irregular Sierpinski gaskets
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 5, pp. 531-557. 
@article{AIHPB_1997__33_5_531_0,
     author = {Barlow, M. T. and Hambly, B. M.},
     title = {Transition density estimates for brownian motion on scale irregular {Sierpinski} gaskets},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {531--557},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {5},
     year = {1997},
     mrnumber = {1473565},
     zbl = {0903.60072},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1997__33_5_531_0/}
}
TY  - JOUR
AU  - Barlow, M. T.
AU  - Hambly, B. M.
TI  - Transition density estimates for brownian motion on scale irregular Sierpinski gaskets
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1997
SP  - 531
EP  - 557
VL  - 33
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1997__33_5_531_0/
LA  - en
ID  - AIHPB_1997__33_5_531_0
ER  - 
%0 Journal Article
%A Barlow, M. T.
%A Hambly, B. M.
%T Transition density estimates for brownian motion on scale irregular Sierpinski gaskets
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1997
%P 531-557
%V 33
%N 5
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1997__33_5_531_0/
%G en
%F AIHPB_1997__33_5_531_0
Barlow, M. T.; Hambly, B. M. Transition density estimates for brownian motion on scale irregular Sierpinski gaskets. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 5, pp. 531-557. http://www.numdam.org/item/AIHPB_1997__33_5_531_0/

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[4] M.T. Barlow and E.A. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Rel. Fields, Vol. 79, 1988, pp. 543-624. | MR | Zbl

[5] A. Beurling and J. Deny, Espaces de Dirichlet I, le cas élémentaire, Acta. Math., Vol. 99, 1958, pp. 203-224. | MR | Zbl

[6] K.J. Falconer, Fractal Geometry, Wiley, Chichester, 1990. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[9] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet forms and symmetric Markov processes, de Gruyter, Berlin, 1994. | MR | Zbl

[10] B.M. Hambly, Brownian motion on a homogeneous random fractal, Probab. Theory Rel. Fields, Vol. 94, 1992, pp. 1-38. | MR | Zbl

[11] B.M. Hambly, Brownian motion on a random recursive Sierpinski gasket, to appear Ann. Probab., 1997. | MR | Zbl

[12] S. Hutchinson, Self-similar sets, Indiana Univ. Math. J., Vol. 30, 1981, pp. 713-747. | Zbl

[13] J. Kigami, A harmonic calculus for p.c.f. self-similar sets, Trans. Am. Math. Soc., Vol. 335, 1993, pp. 721-755. | MR | Zbl

[14] J. Kigami, Harmonic calculus on limits of networks and its applications to dendrites, J. Funct. Anal., Vol. 128, 1995, pp. 48-86. | MR | Zbl

[15] T. Kumagai, Estimates of transition densities for Brownian motion on nested fractals, Proba. Theory Rel. Fields, Vol. 96, 1993, pp. 205-224. | MR | Zbl

[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.

[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. | MR | Zbl

[18] T. Lindstrøm, Brownian motion on nested fractals, Memoirs Am. Math. Soc., Vol. 420, 1990. | MR | Zbl

[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. | MR | Zbl