Journal of Applied Mathematics and Stochastic Analysis 
Volume 12 (1999), Issue 1, Pages 85-90
doi:10.1155/S1048953399000076

Linear filtering with fractional Brownian motion in the signal and observation processes

M. L. Kleptsyna,1 P. E. Kloeden,2 and V. V. Anh3

 1Russian Academy of Sciences, Institute of Information Transmission Problems, Moscow 101447, Russia
2Johan Wolfgang Goethe Universität, Fachbereich Mathematik, Frankfurt D-60054, Germany
3Queensland University of Technology, School of Mathematical Sciences, Brisbane 4001, Australia
Received 1 December 1997; Revised 1 July 1998

Abstract

Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1) and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process.