Ivanov, Ivan; Lomev, Boyan Equilibrium in stochastic Nash games with state-dependent noise via Lyapunov type iterations. (English) Zbl 1214.91008 HERMIS-\(\mu\pi\) 11, 97-101 (2010). Summary: In this paper, the stochastic Nash games for weakly coupled large-scale systems with state-dependent noise are considered. The considered stochastic algebraic Riccati equations are quite different from the existing results in the sense that the equations have the additional linear term. The numerical methods based on the solution of linear matrix equations for solving the cross-coupled stochastic algebraic Riccati equations are introduced. The numerical algorithm that combines Newton’s method with two fixed point algorithms for solving the stochastic algebraic Riccati equations was derived by M. Sagara, H. Mukaidani and T. Yamamoto [Appl. Math. Comput. 197, No. 2, 844–857 (2008; Zbl 1136.91324)]. We consider new iterations based on the solution of linear matrix equations with linear rate of convergence and compare their numerical effectiveness. MSC: 91A15 Stochastic games, stochastic differential games Keywords:cross-coupled stochastic algebraic Riccati equation; Lyapunov equation; positive definite solution Citations:Zbl 1136.91324 PDFBibTeX XMLCite \textit{I. Ivanov} and \textit{B. Lomev}, HERMIS-\(\mu\pi\) 11, 97--101 (2010; Zbl 1214.91008)