Horizons of fractional Brownian surfaces

Kenneth John Falconer, J Lévy Véhel

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We investigate the conjecture that the horizon of an index-alpha fractional Brownian surface has (almost surely) the same Holder exponents as the surface itself, with corresponding relationships for fractal dimensions. We establish this formally for the usual Brownian surface (where alpha = 1/2), and also for other alpha, 0 < alpha < 1, assuming a hypothesis concerning maxima of index-etc Brownian motion. We provide computational evidence that the conjecture is indeed true for all alpha.

Original languageEnglish
Pages (from-to)2153-2178
Number of pages26
JournalProceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Issue number2001
Publication statusPublished - 8 Sept 2000


  • fractal
  • fractional Brownian motion
  • fractional Brownian field
  • horizon
  • dimension


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