Riccati matrix differential equation and the discrete order preserving property

summary:In this paper we recall discrete order preserving property related to the discrete Riccati matrix equation. We present results obtained by applying this property to the solutions of the Riccati matrix differential equation

Stabilita nulového řešení nelineárních diferenciálních rovnic pod vlivem bílého šumu

The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.Článek zkoumá stabilitu nulového řešení nelineárních diferenciálních rovnic pod vlivem bílého šumu