Asymptotically One-Dimensional Diffusions on Scale-Irregular Gaskets
Vol. 4 (1997), No. 2, Page 229--278.
Hattori, Tetsuya
Asymptotically One-Dimensional Diffusions on Scale-Irregular Gaskets
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Abstract:
A new class of fractals, the \rgs, is defined, and the asymptotically one-dimensional diffusion processes are constructed on them. The class contains infinitely many fractals which lack exact self-similarity, and which also lack non-degenerate fixed points of renormalization maps (hence are not in the class of nested fractals). An essential step in the construction of diffusion is to prove the existence of appropriate time-scaling factors. For this purpose, a limit theorem for a discrete-time multi-type supercritical branching processes with singular and irregular (varying) environment, is developed.
Mathematics Subject Classification (1991): Primary 60J60; Secondary 60J25, 60J85, 60J15
Mathematical Reviews Number: MR1466347
Received: 1995-03-07
