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In order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown that this algorithm is monotonically bounded, and the convergence condition is also given and extended. Applying the latest updated estimates, this algorithm can attain a better convergence performance compared with other existing iterative algorithms when choosing appropriate tuning parameters. Finally, a numerical example is provided to illustrate the feasibility and priority of this approach.
Wu et al. (Wed,) studied this question.