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On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation. (English) Zbl 1136.93463

Summary: In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitly the optimal control policy which minimizes an asymptotic quadratic performance criterion.

MSC:

93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
60G15 Gaussian processes
60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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