Journal of Statistical Physics

, Volume 70, Issue 5, pp 1313–1332

Brownian excursions on combs

  • David S. Dean
  • Kalvis M. Jansons

DOI: 10.1007/BF01049434

Cite this article as:
Dean, D.S. & Jansons, K.M. J Stat Phys (1993) 70: 1313. doi:10.1007/BF01049434


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.

Key words

CombstreesBrownian motionIto excursion theoryanomalous diffusion

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • David S. Dean
    • 1
  • Kalvis M. Jansons
    • 2
  1. 1.Department of Applied Mathematics and Theoretical PhysicsCambridge UniversityCambridgeUK
  2. 2.Department of MathematicsUniversity College LondonLondonUK