- 94-152 Hattori T.
- Asymptotically one-dimensional diffusions on scale-irregular gaskets.
(94K, LaTeX Version 2.09 <3 Jan 1988>)
May 31, 94
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Abstract. A simple class of fractals which lack exact self-similarity is introduced,
and the asymptotically one-dimensional diffusion process is constructed.
The process moves mostly horizontally for very small scales, while for large
scales it diffuses almost isotropically, in the sense of the off-horizontal
relative jump rate for the decimated random walks of the process.
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.