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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 1, Pages 23–41
DOI: https://doi.org/10.4213/tvp5259 (Mi tvp5259) 		 
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
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DOI: https://doi.org/10.4213/tvp5259
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.
Funding agency Grant number
Russian Science Foundation 18-71-10097
Received: 18.10.2018
Revised: 30.03.2019
Accepted: 22.05.2019
English version:
Theory of Probability and its Applications, 2020, Volume 65, Issue 1, Pages 17–31
DOI: https://doi.org/10.1137/S0040585X97T989799
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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