Optimal Filtering of Linear System Driven by Fractional Brownian Motion

Abstract

In this paper, we consider a continuous time filtering of a multi-dimensional Langevin stochastic differential system driven by a fractional Brownian motion process. It is shown that this filtering problem is equivalent to an optimal control problem involving convolutional integrals in its dynamical system. Then, a novel approximation scheme is developed and applied to this optimal control problem. It yields a sequence of standard optimal control problems. The convergence of the approximate standard optimal control problem to the optimal control problem involving convolutional integrals in its system dynamics is established. Two numerical examples are solved by using the method proposed. The results obtained clearly demonstrate its efficiency and effectiveness.