Geodesic
On optimal control in the problem of long-run tracking the exponential Ornstein---Uhlenbeck process
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 116-135

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We consider a problem of optimal tracking the exponential Ornstein—Uhlenbeck process. By change of variables, the linear-quadratic control system with discounting has been transformed into linear inhomogeneous system with random coefficients. For such a system, we obtain an optimal control law over an infinite time-horizon. The results are applied to derive an optimal control in the tracking problem with respect to criteria of long-term losses per unit of accumulated discount.
Keywords: linear stochastic controller, tracking, exponential Ornstein—Uhlenbeck process, discounting. . 
@article{SJIM_2022_25_4_a9,
     author = {E. S. Palamarchuk},
     title = {On optimal control in the problem of long-run tracking the exponential {Ornstein---Uhlenbeck} process},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {116--135},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a9/}
}
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E. S. Palamarchuk. On optimal control in the problem of long-run tracking the exponential Ornstein---Uhlenbeck process. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 116-135. http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a9/