Theoretical Statistics and Mathematics Unit, ISI Delhi

Zakai equation of nonlinear filtering with Ornstein-Uhlenbeck noise: Existence and Uniqueness

by Abhay Bhatt, Balram Rajput and Jie Xiong

We consider a filtering model where the noise is an Ornstein-Uhlenbeck process independent of
the signal $X$. The signal is assumed to be a Markov difusion process. We derive the (analogue
of) Zakai equation in this setup. It is a system of two measure valued equations satisfied by the
unnormalised conditional distribution. We also prove uniqueness of solution to these equations.

isid/ms/2002/18 [fulltext]

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