Maximum principle for partial information non-zero sum stochastic differential games with mixed delays

This paper is concerned with one kind of partial information non-zero sum stochastic differential game with mixed delays. Both the state and control processes contain delays, where the former contains moving-average delay, discrete delay and noisy memory. We establish a necessary as well as two sufficient stochastic maximum principles for the game. As one of the main features of this research, a new kind of sufficient maximum principle is given, where the diffusion term can be controlled with non-convex control domains, and no second-order adjoint equation is needed. The theoretical results are applied to study two examples where the adjoint processes can be derived by two approaches and then the equilibrium points are obtained. This research generalizes those of stochastic optimal control problems.