 
Summary: DOI: 10.1007/s0024500207542
Appl Math Optim 46:8188 (2002)
© 2002 SpringerVerlag New York Inc.
Nonlinear Filtering with Fractional Brownian Motion
Anna Amirdjanova
Department of Statistics, University of Michigan,
Ann Arbor, MI 481091092, USA
Abstract. Our objective is to study a nonlinear filtering problem for the observa
tion process perturbed by a Fractional Brownian Motion (FBM) with Hurst index
1
2
< H < 1. A reproducing kernel Hilbert space for the FBM is considered and a
"fractional" Zakai equation for the unnormalized optimal filter is derived.
Key Words. Nonlinear filtering, Fractional Brownian motion, Reproducing kernel
Hilbert space, Stochastic differential equations.
AMS Classification. 60H20, 60G15, 60G35.
1. Introduction
The goal of nonlinear filtering theory is to estimate a signal process (Xt )(0 t T )
observed in the presence of an additive noise. Consider a complete probability space
( , F, P) and a family (Ft )t0 of rightcontinuous increasing Pcomplete subfields
