About this ebook
The purpose of this paper is to construct Brownian motion on a reasonably general class of self-similar fractals. To this end, I introduce an axiomatically defined class of "nested fractals", which satisfy certain symmetry and connectivity conditions, and which also are (in the physicists' terminology) finitely ramified. On each one of these nested fractals, a Brownian motion is constructed and shown to be a strong Markov process with continuous paths.
The purpose of this paper is to construct Brownian motion on a reasonably general class of self-similar fractals. To this end, I introduce an axiomatically defined class of "nested fractals", which satisfy certain symmetry and connectivity conditions, and which also are (in the physicists' termin...
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