  We give a new representation of fractional Brownian motion with Hurst
parameter H<=1/2 using stochastic partial differential equations. This
representation allows us to use the Markov property and time reversal, tools
which are not usually available for fractional Brownian motion. We then give
simple proofs that fractional Brownian motion does not hit points in the
critical dimension, and that it does not have double points in the critical
dimension. These facts were already known, but our proofs are quite simple and
use some ideas of Levy.
