This article is cited in 2 papers

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

DOI: 10.4213/tvp5259

 English version: Theory of Probability and its Applications, 2020, 65:1, 17–31

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