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

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

ESAIM: Probability and Statistics (2003)

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

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topKleptsyna, M. L., Breton, Alain Le, and Viot, M.. "About the linear-quadratic regulator problem under a fractional brownian perturbation." ESAIM: Probability and Statistics 7 (2003): 161-170. <http://eudml.org/doc/245312>.

@article{Kleptsyna2003,

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., Breton, Alain Le, Viot, M.},

journal = {ESAIM: Probability and Statistics},

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

language = {eng},

pages = {161-170},

publisher = {EDP-Sciences},

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

url = {http://eudml.org/doc/245312},

volume = {7},

year = {2003},

}

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

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; linear-quadratic Gaussian regulator

UR - http://eudml.org/doc/245312

ER -

## References

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- [9] 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). Zbl1030.93059MR2148966
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## Citations in EuDML Documents

top- Marina L. Kleptsyna, Alain Le Breton, Michel Viot, On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation
- Marina L. Kleptsyna, Alain Le Breton, Michel Viot, On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
- Marina L. Kleptsyna, Alain Le Breton, Michel Viot, Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation

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