Theory of Probability &Its Applications, Volume 65, Issue 1, Page 17-31, January 2020.
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.

中文翻译：

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基于时变Ornstein-Uhlenbeck过程的积分二次函数的上位函数

概率论及其应用，第65卷，第1期，第17-31页，2020年1月。
我们研究了随时间变化的Ornstein-Uhlenbeck过程定义的积分二次函数的渐近行为。我们发现一个上函数以概率$ 1 $随时间的增加将积分与其期望值的偏差最大化。获得的结果可用于评估渐近稳定控制律在无限时间范围内的随机线性二次调节器的控制性能。