Geodesic
On upper functions for integral quadratic functionals based on time-varying Ornstein--Uhlenbeck process
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 23-41

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We examine the asymptotic behavior of integral quadratic functionals defined on time-varying Ornstein–Uhlenbeck processes. We find an upper function that majorizes with probability 1 the deviation of the integral from its expected value as time increases. The results obtained are applied to evaluate the control performance for stochastic linear-quadratic regulators over an infinite time horizon on asymptotically stable control laws.
Keywords: time-varying Ornstein–Uhlenbeck process, upper function, quadratic functional, asymptotic stability, control, stochastic regulator. 
@article{TVP_2020_65_1_a1,
     author = {E. S. Palamarchuk},
     title = {On upper functions for integral quadratic functionals based on time-varying {Ornstein--Uhlenbeck} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {23--41},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a1/}
}
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E. S. Palamarchuk. On upper functions for integral quadratic functionals based on time-varying Ornstein--Uhlenbeck process. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 23-41. http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a1/