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Maximum Principle for Control System driven by Mixed Fractional Brownian Motion
Yuhang Li, Yuecai Han · 2023-12-19 · via math.PR updates on arXiv.org

In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin calculus and introducing a disturbance control region, we obtain a modified maximum principle. Through martingale representation theorem, we obtain the adjoint backward stochastic differential equation in a natural way. Furthermore, corresponding to [1], a significant result is that the necessary condition is simplified by only containing one equality. As an application, the linear quadratic case is investigated to illustrate the main results.

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