  We show that extremal dynamics is very well modelled by the "Linear
Fractional Stable Motion" (LFSM), a stochastic process entirely defined by two
exponents that take into account spatio-temporal correlations in the
distribution of active sites. We demonstrate this numerically and analytically
using well-known properties of the LFSM. Further, we use this correspondence to
write an exact expressions for an n-point correlation function as well as an
equation of fractional order for interface growth in extremal dynamics.
