Applied Mathematics and Optimization, Vol.46, No.2-3, 81-88, 2002
Nonlinear filtering with fractional Brownian motion
Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1/2 < H < 1. A reproducing kernel Hilbert space for the FBM is considered and a "fractional" Zakai equation for the unnormalized optimal filter is derived.
Keywords:nonlinear filtering;fractional Brownian motion;reproducing kernel Hilbert space;stochastic differential equations