Geodesic
Optimality almost surely and in~probability for a~stochastic linearly quadratic regulator
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 627-632

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The stochastic linear quadratic regulator with constant coefficients is considered in continuous time when the horizon tends to infinity. It is shown that the feedback control, which is optimal for the infinite time horizon in the corresponding deterministic problem is optimal in probability for any rate function which tends to zero and almost sure for any power rate function with negative degree.
Keywords: linear quadratic regulator, optimality almost surely, optimality in probability, stabilizability, detectability. 
@article{TVP_1997_42_3_a14,
     author = {E. L. Presman},
     title = {Optimality almost surely and in~probability for a~stochastic linearly quadratic regulator},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {627--632},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a14/}
}
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E. L. Presman. Optimality almost surely and in~probability for a~stochastic linearly quadratic regulator. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 627-632. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a14/