Optimal filtration for systems with fractional Brownian noises. (Ukrainian, English) Zbl 1123.60024

Posashkov, S. V.

Teor. Jmovirn. Mat. Stat. 72, 120-128 (2005); translation in Theory Probab. Math. Stat. 72, 135-144 (2006).

The author deals with the signal process \(X_t\) and the noise process \(Y_t\) on \([0,T]\) described by the following stochastic equations:
\[ \begin{aligned} X_t&= \eta+\int_0^ta(s,X_s)\,ds+ \sum_{i=1}^N\int_0^tb_i(s)\,dV_s^i,\\ Y_t&=\xi+\int_0^tA(s,X_s)\,ds+ \int_0^tB(s)\,dV_s,\end{aligned} \]
where \(V_s,V_s^i,i=1,\dots,N,\) are fractional Brownian motions with Hurst parameter \(H\in(0.5,1)\). The optimal filtering problem is considered. A system of equations for the optimal filtering is obtained in the case of linear systems.

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

60G35	Signal detection and filtering (aspects of stochastic processes)
60G15	Gaussian processes
60H05	Stochastic integrals
60J65	Brownian motion

Keywords:

filtering; fractional Brownian motion; Hurst parametern t