Pathwise average cost per unit time problem for stochastic differential games with a small parameter

A two person zero-sum stochastic differential game problem for wideband noise driven system is considered. We will consider the payoff structure in the pathwise sense. Under sufficiently general conditions, it will be shown that the optimal equilibrium policies of the limit process when applied to the physical processes, will be ii-equilibrium as the parameters epsilon --> 0 and T --> infinity. Martingale convergence techniques will be used in the analysis. A Chattering result is also derived. The entire problem will be set in relaxed control framework.