基于目标导向相对熵的道路空间模型不确定性量化
Quantification of Model Uncertainty on Path-Space via Goal-Oriented Relative Entropy
摘要：
量化参数和模型形式的不确定性对随机模型预测的影响是许多应用中的关键挑战。以往的工作表明，相对熵率是一个有效的工具，推导道路空间的不确定性量化（UQ）界遍历平均。在这项工作中，我们确定适当的信息理论对象的更广泛的数量感兴趣的道路空间，如首中时和指数折扣可观的，并制定相应的UQ界。此外，我们的方法产生更严格的UQ界限，即使在以前的基于相对熵的方法也适用的情况下，例如，遍历平均数我们从期权定价，不可逆扩散过程，随机控制，半马尔可夫排队模型，和期望和分布的首中时的例子来说明这些结果。
英文摘要：
Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving path-space uncertainty quantification (UQ) bounds on ergodic averages. In this work we identify appropriate information-theoretic objects for a wider range of quantities of interest on path-space, such as hitting times and exponentially discounted observables, and develop the corresponding UQ bounds. In addition, our method yields tighter UQ bounds, even in cases where previous relative-entropy-based methods also apply, e.g., for ergodic averages. We illustrate these results with examples from option pricing, non-reversible diffusion processes, stochastic control, semi-Markov queueing models, and expectations and distributions of hitting times.
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