Non Linear Filtering Theory in Presence of Fractional Brownian Motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion

The problem of optimal ltering is investigated in a continuous time linear Gaussian system where the signal is a xed random variable and the noise driving the observation process is a fractional Brownian motion with Hurst parameter H 2 (1=2; 1). Closed form expressions are derived both for the optimal lter and the variance of the ltering error. Then an application to the determination of the be...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Asymptotically optimal filtering in linear systems with fractional Brownian noises

In this paper, the filtering problem is revisited in the basic Gaussian homogeneous linear system driven by fractional Brownian motions. We exhibit a simple approximate filter which is asymptotically optimal in the sense that, when the observation time tends to infinity, the variance of the corresponding filtering error converges to the same limit as for the exact optimal filter.

On the Infinite Time Horizon Linear-quadratic Regulator Problem under a Fractional Brownian Perturbation

Recently, stochastic models appropriate for long-range dependent phenomena have attracted a great deal of interest and numerous theoretical results and successful applications have been already reported. In particular, several contributions in the literature have been devoted to the extension of the classical theory of continuoustime stochastic systems driven by Brownian motions to analogues in...