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August  2013, 18(6): 1651-1661. doi: 10.3934/dcdsb.2013.18.1651

## Quadratic control problem of neutral Ornstein-Uhlenbeck processes with control delays

 1 Division of Statistics and Probability, Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool, L69 7ZL, United Kingdom

Received  September 2011 Revised  January 2012 Published  March 2013

A class of stochastic optimal control problems of infinite dimensional Ornstein-Uhlenbeck processes of neutral type are considered. One special feature of the system under investigation is that time delays are present in the control. An equivalent formulation between an adjoint stochastic controlled delay differential equation and its lifted control system (without delays) is developed. As a consequence, the finite time quadratic regulator problem governed by this formulation is solved based on a direct solution of some associated Riccati equation.
Citation: Kai Liu. Quadratic control problem of neutral Ornstein-Uhlenbeck processes with control delays. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1651-1661. doi: 10.3934/dcdsb.2013.18.1651
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