Maximum principle for stochastic partial differential system with fractional Brownian motion

Abstract

Fractional Brownian motion (fBm) offers a more precise depiction of intricate dynamic phenomena in real-world scenarios compared to traditional Brownian motion. However, its autocorrelation and non-Markovian properties pose challenges in satisfying the assumptions of conventional mathematical analysis tools and classical stochastic calculus. As a result, modeling and analyzing the optimization problem become difficult. In this paper, we first construct the backward stochastic partial differential equation (BSPDE) with fBm. Then, we focus on obtaining the maximum principle for optimal control of the stochastic partial differential system (SPDS) with fBm by constructing the spike variation process, the first variation equation, and the Hamilton function.