A Nash equilibrium filter

ABSTRACT

The Wonham filter, which estimates a Markov chain observed in Brownian noise, is considered. However, the parameters of the observation process are not known. Maximizing the un-normalized probabilities of the Zakai equation over the parameters leads to a Nash equilibrium whose solution is discussed using the stochastic control results of Peng and Yong and Zhou.

KEYWORDS:

• Markov chain filter
• Nash equilibrium
• maximum principle
• adjoint process

MATHEMATICS SUBJECT CLASSIFICATION:

• 93E11
• 93E20
• 60H15

Funding

The support of the ARO is gratefully acknowledged.