带有分数布朗运动和Markovian调制的随机种群系统的最优逼近控制

Near-optimality in Stochastic Control of Stochastic Age-dependent System with Markovian Switching and Fractional Brownian Motion

讨论了一类带有分数布朗运动和Markovian调制的随机种群系统最优逼近控制问题,给出了模型的伴随方程,哈密顿函数,应用Ekeland变分原理,Ito’s公式及一些不等式等给出了随机种群系统最优逼近控制存在的必要条件.

In this paper,we introduce a class of stochastic age-dependent system with Marvokian switching and fractional Brownian motion,establish necessary for near-optimality.The conditions are described by an adjoint process and a nearly maximum condition on the Hamiltonian.The proof of the main results is based on Ito＇s formula,Ekeland＇s variational principle and some estimates on the state and the adjoint process with respect to the control variable.