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On the infinite time horizon linear-quadratic regulator problem undera fractional Brownian perturbation
Marina L. Kleptsyna, Alain Le Breton, Michel Viot
Journal:

ESAIM: Probability and Statistics / Volume 9 / February 2005

Published online by Cambridge University Press:

15 November 2005, pp. 185-205

Print publication:

February 2005
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In this paper we solve the basic fractionalanalogue of the classical infinite time horizon linear-quadratic Gaussianregulator problem. For a completely observable controlled linearsystem driven by a fractional Brownian motion, we describeexplicitely the optimal control policy which minimizes anasymptotic quadratic performance criterion.