Nonlinear Filtering with Fractional Brownian Motion Noise

Abstract

In this paper, we consider the nonlinear filtering problem for the signal process corrupted by fractional Brownian motion noise. The signal process is assumed to be a Markov diffusion process. We obtain the Zakai equation and the Kushner-FKK equation in this setup. We also prove uniqueness of solution to these equations.

Keywords:

• Fractional Brownian motions
• Kushner-FKK equation
• Martingale problem
• Nonlinear filtering
• Zakai equation

Mathematics Subject Classification:

• 60G35
• 62M20
• 93E11

ACKNOWLEDGMENT

Supported partially by NSA, CRC program, NSERC, Lockheed Martin Naval Electronics and Surveillance Systems, Lockheed Martin Canada, and VisionSmart through a MITACS center of excellence entitled “Prediction in Interacting Systems.”