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quadratic payoff.

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About the linear-quadratic regulator problem under a fractional Brownian perturbation
M. L. Kleptsyna, Alain Le Breton, M. Viot
Journal:

ESAIM: Probability and Statistics / Volume 7 / March 2003

Published online by Cambridge University Press:

15 May 2003, pp. 161-170

Print publication:

March 2003
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In this paper we solve the basic fractionalanalogue of the classical linear-quadratic Gaussianregulator problem in continuous time. For a completelyobservable controlled linear system driven by a fractionalBrownian motion, we describe explicitely the optimal controlpolicy which minimizes a quadratic performance criterion.