On duality between estimation and control for linear stochastic functional evolution equations in Hilbert spaces

摘要

This paper treats a linear least-squares estimation problem in which both the state and observation processes are governed by infinite-dimensional linear stochastic functional evolution equations. The main result obtained in this paper is expressed in terms of a duality principle between the estimation and a linear-quadratic control problem. As a by-product, the representation of the solution process of the equation is also obtained.