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

A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand