L. Coutin, et L. Decreusefond,, Abstract nonlinear filtering theory in the presence of fractional Brownian motion, Annals of applied probability , 9(4), 1999, pp. 1058-1090
We develop the filtering theory in the case where both the signal and the observation are solutions of some stochastic differential equation driven by a multidimensional fractional Brownian motion. We show that the classical approach fails to give a closed equation for the filter and we develop another approach using an auxiliary process-valued semimartingale which solves this problem theoretically.