Pathwise stochastic control with applications to robust filtering
Pathwise stochastic control with applications to robust filtering
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DOI：
10.1214/19-aap1558
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发表时间：
2019-02
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通讯作者：
Andrew L. Allan;Samuel N. Cohen
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文献类型：
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作者：
Andrew L. Allan;Samuel N. Cohen
我们研究了路径随机最优控制问题，其中通过将问题描述为粗糙微分方程的最优控制，对驾驶噪音的每个固定实现进行优化。我们调查的退化现象引起的直接控制噪声项的系数，并提出了一个简单的程序来解决这种退化，同时保留动态规划。作为一个应用程序，我们使用路径随机控制的背景下，随机滤波，构建过滤器是强大的参数不确定性，展示了原始的应用粗糙路径理论的统计。
We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming. As an application, we use pathwise stochastic control in the context of stochastic filtering to construct filters which are robust to parameter uncertainty, demonstrating an original application of rough path theory to statistics.