About the linear-quadratic regulator problem under a fractional brownian perturbation
ESAIM: Probability and Statistics, Volume 7  (2003), p. 161-170

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

DOI : https://doi.org/10.1051/ps:2003007
Classification:  93E20,  60G15,  60G44
Keywords: fractional brownian motion, linear system, optimal control, quadratic payoff
@article{PS_2003__7__161_0,
     author = {Kleptsyna, M. L. and Breton, Alain Le and Viot, M.},
     title = {About the linear-quadratic regulator problem under a fractional brownian perturbation},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     pages = {161-170},
     doi = {10.1051/ps:2003007},
     zbl = {1030.93059},
     mrnumber = {1956077},
     language = {en},
     url = {http://www.numdam.org/item/PS_2003__7__161_0}
}
Kleptsyna, M. L.; Breton, Alain Le; Viot, M. About the linear-quadratic regulator problem under a fractional brownian perturbation. ESAIM: Probability and Statistics, Volume 7 (2003) , pp. 161-170. doi : 10.1051/ps:2003007. http://www.numdam.org/item/PS_2003__7__161_0/

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