Stochastic analysis of fractional brownian motions

In this article some of the important ideas in ordinary stochastic analysis are applied to fractional Brownian motions (fBm's). First we give a simple and elementary proof of the fact that any fBm has zero quadratic variation. This fact leads to the non-semimartingale structure of fBm's. Another consequence is that we can integrate (in probability) the functionals of fBm's with fBm differentials. With the same integrator, we then develop the L2 integration theory of bounded sure processes based on of K. Bichteler's integral extension theory. Finally, we investigate the corresponding stochastic differential equations with fractional Brownian noise