journal article
Mar 01, 1992
Brownian motion on a homogeneous random fractal
Probability Theory and Related Fields
Vol. 94
No. 1
pp. 1-38
·
Springer Science and Business Media LLC
Topics
No keywords indexed for this article. Browse by subject →
References
33
[1]
Athreya, K.B., Ney, P.E.: Branching processes. Berlin Heidelberg New York: Springer 1972
10.1007/978-3-642-65371-1
[2]
Barlow, M.T.: Random walks, electrical resistance and nested fractals. In: Elworthy, K.D., Ikeda, N. (eds.) Asymptotic problems in probability theory. Montreal: Pitman 1992
[3]
Barlow, M.T., Bass, R.F.: Construction of Brownian motion on the Sierpinski carpet. Ann. Inst. H. Poincare25, 225–257 (1989)
[4]
Barlow, M.T., Bass, R.F.: Transition densities for Brownian motion on the Sierpinski carpet. Probab. Theory Relat. Fields91, 307–330 (1992)
10.1007/bf01192060
[5]
Barlow, M.T., Perkins, E.A.: Brownian motion on the Sierpinski gasket. Probab. Theory Relat. Fields79, 543–624 (1988)
10.1007/bf00318785
[6]
Doyle, P.G., Snell, J.L.: Random walks and electric networks. (Carus Math., Monogr., vol. 22) Washington: Mathematical Association of America 1984
10.5948/upo9781614440222
[7]
Falconer, K.: Fractal geometry, mathematical foundations and applications New York: Wiley 1990
[8]
Feller, W., McKean, H.P.: A diffusion equivalent to a countable Markov chain. Proc. Natl. Acad. Sci., USA42, 351–354 (1956)
10.1073/pnas.42.6.351
[9]
Freedman, D.: Brownian motion and diffusion. San Francisco: Holden-Day 1971
[10]
Freedman, D.: Approximating countable Markov chains. San Francisco: Holden-Day 1971
[11]
Fukushima, M.: Dirichlet forms and Markov processes. Amsterdam: North-Holland 1980
[12]
Fukushima, M.: Dirichlet forms, diffusion processes and spectral dimensions for nested fractals. (Preprint 1991)
[13]
Fukushima, M., Shima, T.: On a spectral analysis for the Sierpinski gasket. J. Potential Anal. (to appear)
[14]
Goldstein, S.: Random walks and diffusions on fractals. In: Kesten, H. (ed.) Percolation theory and, ergodic theory of interacting particle systems, pp. 121–129. Berlin Heidelberg New York: Springer 1987
10.1007/978-1-4613-8734-3_8
[15]
Hambly, B.M.: A diffusion on a class of random fractals. PhD thesis., Cambridge: University of Cambridge 1990
[16]
Hambly, B.M.: On the limiting distribution of a supercritical branching process in a random environment. J. Appl. Probab. (to appear 1992)
10.1017/s0021900200043345
[17]
Havlin, S., Ben-Avraham, D.: Diffusion in disordered media Adv. Phys.36, 695–798 (1987)
10.1080/00018738700101072
[19]
Ito, K., McKean, H.P.: Diffusion processes and their sample paths. Berlin Heidelberg New York: Springer 1965
[20]
Kigami, J.: A harmonic calculus on the Sierpinski spaces. Japan J. Appl. Math.6, 259–290 (1989)
10.1007/bf03167882
[21]
Kigami, J.: Harmonic calculus on p.c.f. self-similar sets. (Preprint 1990)
[22]
Krebs, W.B.: A diffusion defined on a fractal state space. PhD thesis, University of California, Berkeley (1988)
[23]
Kusuoka, S.: A diffusion process on a fractal. In: Ikeda, N., Ito, K. (eds.) Probabilistic methods in mathematical physics. Taniguchi symposium Katata 1985, p. 251–274. Tokyo Amsterdam: Kino Kuniya-Norht Holland 1987
[24]
Kusuoka, S.: Dirichlet forms on fractals and products of random matrices. Publ. Res. Inst. Math. Sci.25, 659–680 (1989)
10.2977/prims/1195173187
[25]
Rogers, L.C.G., Williams, D.: Construction and approximation of transition matrix functions. Adv. Appl. Probab. Suppl. 133–160 (1986)
[26]
Lindstrom, T.: Brownian motion on nested fractals Mem. Am. Math. Soc.420 (1990)
10.1090/memo/0420
[27]
Marcus, M.B., Rosen, J.: Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes. Ann. Probab. (to appear 1992)
10.1214/aop/1176989524
[28]
Milosevic, S., Stassinopoulos, D., Stanley, H.E.: Asymptotic behaviour of the spectral dimension at the fractal to lattice crossover. J. Phys. A21, 1477–1482 (1988)
10.1088/0305-4470/21/6/024
[29]
Rammal, R., Toulouse, G.: Random walks on fractal structures and percolation clusters. J. Phys. Lett.44, L13-L21 (1983)
10.1051/jphyslet:0198300440101300
[30]
Shima, T.: On Eigenvalue problems for random walks on the Sierpinski pregaskets. Japan J. Appl. Math. (to appear)
[31]
Taylor, S.J.: On the measure theory of random fractals. Proc. Cam. Philos. Soc.100, 345–367 (1987)
[32]
Telcs, A.: Random walks, graphs and electric networks Probab. Theory Relat. Fields83, 245–264 (1989)
[33]
Williams, D.: Diffusion, Markov processes and martingales. New York: Wiley 1979
Metrics
50
Citations
33
References
Details
- Published
- Mar 01, 1992
- Vol/Issue
- 94(1)
- Pages
- 1-38
- License
- View
Authors
Cite This Article
B. M. Hambly (1992). Brownian motion on a homogeneous random fractal. Probability Theory and Related Fields, 94(1), 1-38. https://doi.org/10.1007/bf01222507
Related
You May Also Like
On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier, Arnaud Guillin · 2014
671 citations
Forward-backward stochastic differential equations and quasilinear parabolic PDEs
Etienne Pardoux, Shanjian Tang · 1999
245 citations
Time-fractional telegraph equations and telegraph processes with brownian time
Enzo Orsingher, Luisa Beghin · 2003
239 citations