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

Abstract

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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.

How to cite

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Kleptsyna, 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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  6. M.L. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Statist. Inference Stochastic Process. (to appear).  
  7. 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).  
  8. 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.  
  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).  
  10. R.S. Liptser and A.N. Shiryaev, Statistics of Random Processes. Springer-Verlag (1978).  
  11. 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.  
  12. 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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