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This article is cited in 1 scientific paper (total in 1 paper)
On upper functions for integral quadratic functionals based on time-varying Ornstein–Uhlenbeck process
E. S. Palamarchuk Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
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.
Received: 18.10.2018 Revised: 30.03.2019 Accepted: 22.05.2019
Citation:
E. S. Palamarchuk, “On upper functions for integral quadratic functionals based on time-varying Ornstein–Uhlenbeck process”, Teor. Veroyatnost. i Primenen., 65:1 (2020), 23–41; Theory Probab. Appl., 65:1 (2020), 17–31
Linking options:
https://www.mathnet.ru/eng/tvp5259https://doi.org/10.4213/tvp5259 https://www.mathnet.ru/eng/tvp/v65/i1/p23
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Abstract page: | 280 | Full-text PDF : | 48 | References: | 32 | First page: | 5 |
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