非对称的Richard模型的平均期望费用问题  

Average expected cost of nonsymmetric Richard model

作　　者：田绍琳[1] 刘坤会[1] 赵生变[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《哈尔滨工程大学学报》2007年第12期1391-1396,共6页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(19671004);北京交通大学博士生科技创新基金资助项目(20051015)

摘　　要：针对的Richard模型的平稳问题进行了深入的研究,对原模型的费用函数做了进一步推广,将Richard模型的费用函数从对称的情况推广为非对称的情况,使模型中的函数满足更一般的条件.应用了随机分析、高等概率、随机过程和现代鞅论等方法,对推广后的模型给出了最优解的解析式,求得了最佳控制ξ*、控制区间[c′,c]、常数λ.由于费用函数的非对称性特征,解决了随机控制模型的一类问题,而且该模型有更加广泛的应用前景.There have been many studies on discounted expenses with the Richard model to date, but only a few involve steady problems. In this paper, we study a class of steady problems related to the Richard model, and make a further extension to cost functions in the model. Due to the extension, the cost function in the Richard model becomes suitable for both symmetric and nonsymmetric conditions, so that it can meet more general conditions of the model. By using methods such as stochastic analysis, advanced probability theory, the stochastic process, and modern martingale theory, the optimal analytical solution was found for the extended model, and the optimal control and control interval were derived. Because the cost function is nonsymmetric, the extended model successfully resolves problems related to stochastic control and also provides wider prospects for the application of this model.

关 键 词：Richard模型 脉冲控制 变分方程 随机微分方程 随机分析 鞅 

分 类 号：O211.6[理学—概率论与数理统计]