Abstract
A two person, zero-sum, noncooperative stochastic differential game is formulated and solved for a multidimensional linear stochastic system that has a quadratic payoff and a linear state dependent scalar fractional Brownian motion noise process in the stochastic system. The strategies are restricted to be linear feedback. A Riccati equation is given that provides the optimal control strategies for the two players using a direct method and this Riccati equation is different from the one for the corresponding problem with an additive Brownian motion. The strategies are shown to form a Nash equilibrium. The method presented and applied here for the solution requires only some elementary notions from a stochastic calculus for a fractional Brownian motion.
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