TITLE

Fractional Brownian Vector Fields

SPEAKER

Pouya Dehghani Tafti, BIG, EPFL, Switzerland

ABSTRACT

We propose a vector generalisation of fractional Brownian motion that takes
account of directional properties of vector fields such as curl and
divergence, which have no counterpart in the scalar setting.  In addition to
the Hurst exponent that describes the scaling behaviour of the model, we
define additional parameters that encode irrotational vs solenoidal
tendencies.  We give a characterisation of the proposed random fields as
solutions of a fractional PDE with white noise as the driving term, where the
fractional differential operator in question is identified on the basis of its
invariance with respect to specific coordinate transformations (rotation and
scaling).  We then review some of the properties of these models which can be
of interest in applications.