一类广告的随机最优控制模型的奇摄动解
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摘要
讨论随机情形下广告投入的最优控制问题,应用最优控制原理得到关于广告投入的奇异摄动随机最优控制问题的HJB方程,利用奇摄动渐近展开的方法得到HJB方程的形式渐近解,并得到其一致有效估计.
A class of stochastic singular perturbation optimal control problem is discussed in this paper.Using the Kolmogorov equation,Hamilton-Jacobi-Bellman equation of the stochastic singular perturbation optimal control problem for advertising investment is achieved.Using the singular perturbation asymptotic expansion method,the formal asymptotic expansion is obtained.And the uniform valid estimation of the formal asymptotic expansion is derived.
A class of stochastic singular perturbation optimal control problem is discussed in this paper.Using the Kolmogorov equation,Hamilton-Jacobi-Bellman equation of the stochastic singular perturbation optimal control problem for advertising investment is achieved.Using the singular perturbation asymptotic expansion method,the formal asymptotic expansion is obtained.And the uniform valid estimation of the formal asymptotic expansion is derived.
引文
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[7]WU L M,NI M K,LU H B.Internal transition layer solution of singularly perturbed optimal control problem[J].Acta Mathematica Scientia,2013,33(2):206-215.
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[9]SCHMIDLI H.Stochastic Control in Continuous Time[M]//Stochastic Control in Insurance.London:Springer,2008:27-111.
[2]王秀青,蔡立军.竞争环境下的广告策略研究[J].纺织高校基础科学学报,2009,22(3):404-408.
[3]陈丽.时滞随机系统的最优控制问题及应用[D].济南:山东大学,2010.
[4]丁海云,倪明康.函数不连续的二阶拟线性奇摄动边值问题[J].纯粹数学与应用数学,2010,26(5):768-775.
[5]丁海云,倪明康.具有不连续源的奇摄动边值问题[J].数学杂志,2012,32(6):1121-1128.
[6]WU L M,NI M K,LU H B.Step-like contrast structures of singularly perturbed optimal control problem[J].Journal of Computational Mathematics,2012,30(1):2-13.
[7]WU L M,NI M K,LU H B.Internal transition layer solution of singularly perturbed optimal control problem[J].Acta Mathematica Scientia,2013,33(2):206-215.
[8]ZHANG Y,NAIDU D S,CAI C X,et al.Singular perturbations and time scales in control theories and applications:on overview 2002-2012[J].International Journal of Informational and systems sciences,2014,9(1):1-36.
[9]SCHMIDLI H.Stochastic Control in Continuous Time[M]//Stochastic Control in Insurance.London:Springer,2008:27-111.