On the Zakai equation of filtering with Gaussian noise
Stochastics in Finite and Infinite Dimensions
The purpose of this work is to present an analogue of the Zakai type equation in case the noise is a Gaussian process, including fractional Brownian motion (fBm). The problem is of interest in view of the fact that the signal sent through the internet is contaminated by the noise given by fBm (). Recently, a similar filtering problem with fBm noise was considered in . However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([11, 5]).
Print ISBN 978-1-4612-6643-3 Online ISBN 978-1-4612-0167-0
© 2001 Springer Science+Business Media New York
Gawarecki, Leszek and Mandrekar, Vidyadhar S., "On the Zakai equation of filtering with Gaussian noise" (2001). Mathematics Publications. 15.