 94152 Hattori T.
 Asymptotically onedimensional diffusions on scaleirregular gaskets.
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May 31, 94

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Abstract. A simple class of fractals which lack exact selfsimilarity is introduced,
and the asymptotically onedimensional 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 offhorizontal
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 timescaling factors. For this purpose, a limit theorem for
a discretetime multitype supercritical branching processes with
singular and irregular (varying) environment, is developed.
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