Hattori T.
Asymptotically one-dimensional diffusions on scale-irregular gaskets.
(94K, LaTeX Version 2.09 <3 Jan 1988>)
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.