# About the linear-quadratic regulator problem under a fractional Brownian perturbation

M. L. Kleptsyna; Alain Le Breton; M. Viot

ESAIM: Probability and Statistics (2010)

- Volume: 7, page 161-170
- ISSN: 1292-8100

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topKleptsyna, M. L., Le Breton, Alain, and Viot, M.. "About the linear-quadratic regulator problem under a fractional Brownian perturbation." ESAIM: Probability and Statistics 7 (2010): 161-170. <http://eudml.org/doc/104301>.

@article{Kleptsyna2010,

abstract = {
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.
},

author = {Kleptsyna, M. L., Le Breton, Alain, Viot, M.},

journal = {ESAIM: Probability and Statistics},

keywords = {Fractional Brownian motion; linear system;
optimal control; quadratic payoff.; fractional Brownian motion; optimal control; quadratic payoff; linear-quadratic Gaussian regulator},

language = {eng},

month = {3},

pages = {161-170},

publisher = {EDP Sciences},

title = {About the linear-quadratic regulator problem under a fractional Brownian perturbation},

url = {http://eudml.org/doc/104301},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Kleptsyna, M. L.

AU - Le Breton, Alain

AU - Viot, M.

TI - About the linear-quadratic regulator problem under a fractional Brownian perturbation

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 161

EP - 170

AB -
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.

LA - eng

KW - Fractional Brownian motion; linear system;
optimal control; quadratic payoff.; fractional Brownian motion; optimal control; quadratic payoff; linear-quadratic Gaussian regulator

UR - http://eudml.org/doc/104301

ER -

## References

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- M.L. Kleptsyna and A. Le Breton, Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises. Statist. Inference Stochastic Process. (to appear).
- M.L. Kleptsyna, A. Le Breton and M.-C. Roubaud, General approach to filtering with fractional Brownian noises - Application to linear systems. Stochastics and Stochastics Rep.71 (2000) 119-140.
- M.L. Kleptsyna, A. Le Breton and M. Viot, 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).
- R.S. Liptser and A.N. Shiryaev, Statistics of Random Processes. Springer-Verlag (1978).
- I. Norros, E. Valkeila and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli5 (1999) 571-587.
- C.J. Nuzman and H.V. Poor, Linear estimation of self-similar processes via Lamperti's transformation. J. Appl. Probab.37 (2000) 429-452.

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