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

Mandl, Petr

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

Keywords:

linear diffusion process; controlled drift; quadratic cost; asymptotic behaviour; Riccati equation; time-invariant

Citations:

Zbl 0619.00019