Brownian Motion on Nested Fractals (Memoirs of the American Mathematical Society)

Tom Lindstrøm. January 1990, Volume 83, Number 420 (second Of 6 Numbers). Includes Bibliographical References. 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