一类半鞅状态的平稳型脉冲随机控制

A CLASS OF STATIONARY IMPULSE STOCHASTIC CONTROL WITH STATE OF SEMI-MARTINGALE

本文提出了一类新的随机控制模型,这类模型不但在费用结构上推广了此前的平稳型脉冲随机控制,而且首次将一类半鞅引入脉冲控制模型的状态结构从而推广了相应的状态过程.通过对一类相当复杂的变分方程问题的研究并利用其有关结论,我们证明了新模型最佳控制的存在性并刻划出其结构.

This paper gives a new stochastic control model, this model not only extends the past stationary impulse stochastic control on cost structure, but also first introduces a class of Semi-Martingale into impulse control model and extends its state process. From studying some kind of quite complex variational equation problems and applying the conclusion, we prove that the optimal control of new model is existent and characterize its structure.