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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

Citations:

Zbl 0619.00019