Summary: DOI: 10.1007/s00245-002-0754-2
Appl Math Optim 46:8188 (2002)
© 2002 Springer-Verlag New York Inc.
Nonlinear Filtering with Fractional Brownian Motion
Department of Statistics, University of Michigan,
Ann Arbor, MI 48109-1092, 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
< 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.
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 right-continuous increasing P-complete sub--fields