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Volumn 15, Issue 2, 2002, Pages 285-322

Asymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment

Author keywords

Branching process; Diffusion; Fractal; Heat kernel; Multi type; Sierpinski gasket; Spectral dimension; Varying environment

Indexed keywords


EID: 0036302828     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014858709284     Document Type: Article
Times cited : (10)

References (17)
  • 2
    • 0001035130 scopus 로고
    • The construction of Brownian motion on the Sierpinski carpet
    • Barlow, M. T., and Bass, R. F. (1989). The construction of Brownian motion on the Sierpinski carpet. Ann. Inst. Henri Poincaré 25, 225-257.
    • (1989) Ann. Inst. Henri Poincaré , vol.25 , pp. 225-257
    • Barlow, M.T.1    Bass, R.F.2
  • 3
    • 0031537272 scopus 로고    scopus 로고
    • Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets
    • Barlow, M. T., and Hambly, B. M. (1997). Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets. Ann. Inst. H. Poincare, 33, 531-557.
    • (1997) Ann. Inst. H. Poincare , vol.33 , pp. 531-557
    • Barlow, M.T.1    Hambly, B.M.2
  • 5
    • 0001352912 scopus 로고    scopus 로고
    • Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets
    • Barlow, M. T., and Kigami, J. (1997). Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets. J. London Math. Soc. 56, 320-332.
    • (1997) J. London Math. Soc. , vol.56 , pp. 320-332
    • Barlow, M.T.1    Kigami, J.2
  • 6
    • 0000459757 scopus 로고
    • On the limit of a supercritical branching process
    • Bingham, N. H. (1988). On the limit of a supercritical branching process. J. Appl. Prob. A 25, 215-228.
    • (1988) J. Appl. Prob. A , vol.25 , pp. 215-228
    • Bingham, N.H.1
  • 7
    • 0001635191 scopus 로고
    • On products of non-negative matrices
    • Cohn, H., and Nerman, O. (1990). On products of non-negative matrices. Ann. Probab. 18, 1806-1815.
    • (1990) Ann. Probab. , vol.18 , pp. 1806-1815
    • Cohn, H.1    Nerman, O.2
  • 8
    • 21844490714 scopus 로고
    • Transition density estimates for Brownian motion on affine nested fractals
    • Fitzsimmons, P. J., Hambly, B. M., and Kumagai, T. (1994). Transition density estimates for Brownian motion on affine nested fractals. Commun. Math. Phys. 165, 595-620.
    • (1994) Commun. Math. Phys. , vol.165 , pp. 595-620
    • Fitzsimmons, P.J.1    Hambly, B.M.2    Kumagai, T.3
  • 9
    • 0002832308 scopus 로고
    • On a spectral analysis for the Sierpinski gasket
    • Fukushima, M., and Shima, T. (1992). On a spectral analysis for the Sierpinski gasket. Potential Anal. 1, 1-35.
    • (1992) Potential Anal. , vol.1 , pp. 1-35
    • Fukushima, M.1    Shima, T.2
  • 10
    • 0032377831 scopus 로고    scopus 로고
    • Heat kernel estimates and homogenization for asymptotically lower dimensional processes on some nested fractals
    • Hambly, B. M., and Kumagai, T. (1998). Heat kernel estimates and homogenization for asymptotically lower dimensional processes on some nested fractals. Potential Anal. 8, 359-397.
    • (1998) Potential Anal. , vol.8 , pp. 359-397
    • Hambly, B.M.1    Kumagai, T.2
  • 11
    • 0001569543 scopus 로고    scopus 로고
    • Transition density estimates for diffusions on p.c.f. self-similar fractals
    • Hambly, B. M., and Kumagai, T. (1999). Transition density estimates for diffusions on p.c.f. self-similar fractals. Proc. London Math. Soc. (3) 78, 431-458.
    • (1999) Proc. London Math. Soc. (3) , vol.78 , pp. 431-458
    • Hambly, B.M.1    Kumagai, T.2
  • 12
    • 21844485200 scopus 로고
    • Asymptotically one-dimensional diffusions on the Sierpinski gasket and the abc-gaskets
    • Hattori, K., Hattori, T., and Watanabe, H. (1994). Asymptotically one-dimensional diffusions on the Sierpinski gasket and the abc-gaskets. Probab. Theory Related Fields 100, 85-116.
    • (1994) Probab. Theory Related Fields , vol.100 , pp. 85-116
    • Hattori, K.1    Hattori, T.2    Watanabe, H.3
  • 13
    • 0009030655 scopus 로고    scopus 로고
    • Asymptotically one dimensional diffusions on scale-irregular gaskets
    • Hattori, T. (1997). Asymptotically one dimensional diffusions on scale-irregular gaskets. J. Math. Sci. Univ. Tokyo 4, 229-278.
    • (1997) J. Math. Sci. Univ. Tokyo , vol.4 , pp. 229-278
    • Hattori, T.1
  • 14
    • 0031184715 scopus 로고    scopus 로고
    • Anisotropic random walks and asymptotically one-dimensional diffusion on abc-gaskets
    • Hattori, T., and Watanabe, H. (1997). Anisotropic random walks and asymptotically one-dimensional diffusion on abc-gaskets. J. Stat. Phys. 88, 105-128.
    • (1997) J. Stat. Phys. , vol.88 , pp. 105-128
    • Hattori, T.1    Watanabe, H.2
  • 16
    • 0031502804 scopus 로고    scopus 로고
    • On the convergence of multi-type branching processes with varying environments
    • Jones, O. D. (1997). On the convergence of multi-type branching processes with varying environments. Ann. Appl. Probab. 7, 772-801.
    • (1997) Ann. Appl. Probab. , vol.7 , pp. 772-801
    • Jones, O.D.1
  • 17
    • 21144470507 scopus 로고
    • Estimates of the transition densities for Brownian motion on nested fractals
    • Kumagai, T. (1993). Estimates of the transition densities for Brownian motion on nested fractals. Probab. Theory Related Fields 96, 205-224.
    • (1993) Probab. Theory Related Fields , vol.96 , pp. 205-224
    • Kumagai, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.