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.
Mots clés : 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},
pages = {161--170},
publisher = {EDP-Sciences},
volume = {7},
year = {2003},
doi = {10.1051/ps:2003007},
mrnumber = {1956077},
zbl = {1030.93059},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2003007/}
}
TY - JOUR AU - Kleptsyna, M. L. AU - Breton, Alain Le AU - Viot, M. TI - About the linear-quadratic regulator problem under a fractional brownian perturbation JO - ESAIM: Probability and Statistics PY - 2003 SP - 161 EP - 170 VL - 7 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2003007/ DO - 10.1051/ps:2003007 LA - en ID - PS_2003__7__161_0 ER -
%0 Journal Article %A Kleptsyna, M. L. %A Breton, Alain Le %A Viot, M. %T About the linear-quadratic regulator problem under a fractional brownian perturbation %J ESAIM: Probability and Statistics %D 2003 %P 161-170 %V 7 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2003007/ %R 10.1051/ps:2003007 %G en %F 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, Tome 7 (2003), pp. 161-170. doi : 10.1051/ps:2003007. http://www.numdam.org/articles/10.1051/ps:2003007/
[1] , Linear Estimation and Stochastic Control. Chapman and Hall (1977). | MR | Zbl
[2] and, Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177-214. | MR | Zbl
[3] , and, Stochastic calculus for fractional Brownian motion I. Theory. SIAM J. Control Optim. 38 (2000) 582-612. | MR | Zbl
[4] and, On the prediction of fractional Brownian motion. J. Appl. Probab. 33 (1997) 400-410. | MR | Zbl
[5] , and, A stochastic maximum principle for processes driven by fractional Brownian motion, Preprint 24. Pure Math. Dep. Oslo University (2000).
[6] and, Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Statist. Inference Stochastic Process. (to appear). | Zbl
[7] and, Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises. Statist. Inference Stochastic Process. (to appear). | Zbl
[8] , and, General approach to filtering with fractional Brownian noises - Application to linear systems. Stochastics and Stochastics Rep. 71 (2000) 119-140. | Zbl
[9] , and, Solution of some linear-quadratic regulator problem under a fractional Brownian perturbation and complete observation, in Prob. Theory and Math. Stat., Proc. of the 8th Vilnius Conference, edited by B. Grigelionis et al., VSP/TEV (to appear).
[10] and, Statistics of Random Processes. Springer-Verlag (1978). | Zbl
[11] , and, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli 5 (1999) 571-587. | MR | Zbl
[12] and, Linear estimation of self-similar processes via Lamperti's transformation. J. Appl. Probab. 37 (2000) 429-452. | MR | Zbl
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