## Limit theorems of probability theory and optimality in linear controlled systems with quadratic cost.(English)Zbl 0637.93078

Stochastic differential systems, Proc. IFIP-WG 7/1 Work. Conf., Eisenach/GDR 1986, Lect. Notes Control Inf. Sci. 96, 316-329 (1987).
[For the entire collection see Zbl 0619.00019.]
A linear diffusion process with controlled drift and quadratic cost $$C_ T$$, $$T>0$$ is considered. The asymptotic behaviour of $(1/T)\int^{T}_{0}1_{\{C_ t>\theta t\}}dt,\quad (C_ T-\theta T)/\sqrt{2T \log \log T},\quad T\to \infty$ is described for a wide class of controls, where $$\theta =\lim_{T\to \infty} C_ T/T$$ a.s. is a parameter defined by terms of the corresponding Riccati equation.
Reviewer: H.Pragarauskas

### MSC:

 93E20 Optimal stochastic control 60F99 Limit theorems in probability theory 60J60 Diffusion processes 93C05 Linear systems in control theory

Zbl 0619.00019