Infinite time nonzero-sum linear quadratic stochastic differential games

In this paper, we deal with the problem of infinite time nonzero-sum linear quadratic differential games of the stochastic system governed by Itô-type equation with state noise. Combining the stochastic exact observability or exact detectability with the stochastic differential games, some theorems are obtained that show the optimal strategies and the optimal cost values are associated with four coupled equations. Finally, a numerical example is given to demonstrate our results.