| 引用本文: | 于洋,王秋媛,赵生变.一类具有漂移、扩散及停时的奇异型随机控制[J].控制理论与应用,2010,27(4):431~436.[点击复制] |
| YU Yang,WANG Qiu-yuan,ZHAO Sheng-bian.Problems of singular stochastic control with stopping, drift and diffusion[J].Control Theory and Technology,2010,27(4):431~436.[点击复制] |
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| 一类具有漂移、扩散及停时的奇异型随机控制 |
| Problems of singular stochastic control with stopping, drift and diffusion |
| 摘要点击 2012 全文点击 870 投稿时间：2008-06-18 修订日期：2009-04-28 |
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| DOI编号 10.7641/j.issn.1000-8152.2010.4.CCTA080631 |
| 2010,27(4):431-436 |
| 中文关键词 随机控制 停时 奇异型控制 漂移 扩散 |
| 英文关键词 stochastic control stopping time singular control drift diffusion |
| 基金项目 国家自然科学基金资助项目(70471001); 国家自然科学基金资助项目(70771006); 北京交通大学校基金资助项目(2006XM044). |
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| 中文摘要 |
| 以随机分析的知识和最优控制理论为基础, 推广了一类带停时的奇异型随机控制中的折扣费用模型, 主要在受控状态过程中增加了漂移因子和扩散因子, 使其为一随机微分方程的解, 并将费用函数一般化. 通过求解一组变分方程, 证明了最优控制及最优停时的存在性, 并给出了最优费用函数的解析表达式. |
| 英文摘要 |
| Based on the stochastic calculus and the classical theory of optimal control, this paper generalizes a class of the discounted model of singular stochastic control with stopping time. Drift and diffusion coefficients are introduced into
the controlled states to make them the solution of a stochastic differential equation. Meanwhile, the cost function is also generalized. By solving a variational equation, we prove the existence of the optimal control and the optimal stopping time. Moreover, we derive the explicit form for the optimal cost function. |
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