Horizons of fractional Brownian surfaces (Q2706723)

The authors investigate the conjecture that the horizon of an index-\(\alpha\) fractional Brownian surface has (almost surely) the same Hölder exponents as the surface itself, with corresponding relationships for fractal dimensions. They establish this formally for the usual Brownian surface (where \(\alpha=\frac 12\)), and also for other \(\alpha\), \(0<\alpha<1\), assuming a hypothesis concerning maxima of index-\(\alpha\) Brownian motion. At the end of the paper they provide computational evidence that the conjecture is indeed true for all \(\alpha\).