On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation
ESAIM: Probability and Statistics, Tome 9 (2005), pp. 185-205.

In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic gaussian regulator problem. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.

DOI : 10.1051/ps:2005008
Classification : 60G15, 60G44, 93E20
Mots clés : fractional brownian motion, linear system, optimal control, quadratic payoff, infinite time 
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     title = {On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation},
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Kleptsyna, Marina L.; Breton, Alain Le; Viot, Michel. On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation. ESAIM: Probability and Statistics, Tome 9 (2005), pp. 185-205. doi : 10.1051/ps:2005008. http://archive.numdam.org/articles/10.1051/ps:2005008/

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