Abstract
In this paper we use techniques from Ito excursion theory to analyze Brownian motion on generalized combs. Ito excursion theory is a little-known area of probability theory and we therefore present a brief introduction for the uninitiated. A general method for analyzing transport along the backbone of the comb is demonstrated and the specific case of a comb whose teeth are scaling branching trees is examined. We then present a recursive method for evaluating the distribution of the first passage times on hierarchical combs.
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Dean, D.S., Jansons, K.M. Brownian excursions on combs. J Stat Phys 70, 1313–1332 (1993). https://doi.org/10.1007/BF01049434
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DOI: https://doi.org/10.1007/BF01049434