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

Copyright © 1999 M. L. Kleptsyna et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.