Linear filtering with fractional noises: large time and small noise asymptotics

We consider a basic Kalman-Bucy model with noises, generated by independent fractional Brownian motions, and develop a new method of asymptotic analysis of the integro-differential filtering equation arising in this case. We establish existence of the steady-state error limit and find its asymptotic scaling in the high signal-to-noise regime. Closed form expressions are derived in a number of important cases.

(Joint job with P. Chigansky, D. Afterman and D. Marushkevych.)