On uniqueness of strong solution of stochastic systems
Summary: A kind of the well-known matrix Riccati equations which arise in certain stochastic optimal problems is investigated. With the aid of the operator spectrum and the generalized Lyapunov equation approach, we give a sufficient condition for existence and uniqueness of the strong solution related to the critical mean square stabilization of stochastic linear controlled systems, which proves Conjecture 10 in [\textit{W. Zhang} et al., IEEE Trans. Autom. Control 53, No. 7, 1630--1642 (2008; Zbl 1367.93549)] to a large extent. In addition, we get some properties of the strong solution. At last, we give a kind of stochastic system which has only a strong solution by an example.
scientific article; zbMATH DE number 7023247
scientific article