Optimal control of stochastic system with Fractional Brownian Motion

In this paper, we introduce a class of stochastic harvesting population system with Fractional Brownian Motion (FBM), which is still unclear when the stochastic noise has the character of memorability. Stochastic optimal control problems with FBM can not be studied using classical methods, because FBM is neither a Markov pocess nor a semi-martingale. When the external environment impact on the system of FBM, the necessary and sufficient conditions for the optimization are offered through the stochastic maximum principle, Hamilton function and Ito formula in our work. To illustrate our study, we provide an example to demonstrate the obtained theoretical results, which is the expansion of certainty population system.

Automated summary

This paper introduces a class of stochastic harvesting population system with Fractional Brownian Motion (FBM) and discusses the conditions for optimization when the system has stochastic noise with memorability. The study presents necessary and sufficient conditions for optimization using stochastic maximum principle, Hamilton function and Ito formula when the external environment impacts the FBM system. An example is provided to demonstrate the obtained theoretical results, which extends the certainty population system.