journal6 ›› 2013, Vol. 34 ›› Issue (2): 5-11.DOI: 10.3969/j.issn.1007-2985.2013.02.002

• 数学 • 上一篇    下一篇

带分数布朗运动和Markovian跳的种群系统的近优控制

  

  1. (宁夏大学数学计算机学院,宁夏 银川 750021)
  • 出版日期:2013-03-25 发布日期:2013-04-23
  • 作者简介:张启敏(1964-),女,天津人,宁夏大学数学计算机学院教授,博士,博士生导师,主要从事随机计算及其应用研究.
  • 基金资助:

    国家自然科学基金资助项目(11061024;11261043)

Near-Optimality in Stochastic Control of Stochastic Age-Dependent System with Markovian Switching and Fractional Brownian Motion

  1. (School of Mathematics and Computer Science,Ningxia University,Yinchuan 750021,China)
  • Online:2013-03-25 Published:2013-04-23

摘要: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公式及一些不等式给出了随机种群系统最优逼近控制存在的必要条件.

关键词: 随机种群, 分数布朗运动, Markovian链, 最优逼近控制, Ekeland变分

Abstract: A class of stochastic age-dependent system with Marvokian switching and fractional Brownian motion is introduced,and the necessary conditions for near-optimality are established.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 formula,Ekeland’s variational principle and some estimates on the state and the adjoint process with respect to the control variable.

Key words: stochastic age-dependent system, fractional Brownian motion, markovian switching, near-optimal, ekeland&rsquo, s variational principle

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