We consider the problem of filtering an unseen Markov chain from noisy observations, in the presence of uncertainty regarding the parameters of the processes involved. Using the theory of nonlinear expectations, we describe the uncertainty in terms of a penalty function, which can be propagated forward in time in the place of the filter. We also investigate a simple control problem in this context.

中文翻译：

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离散时间的隐马尔可夫模型的不确定性和滤波

我们考虑在涉及的过程参数存在不确定性的情况下，从噪声观测中过滤掉看不见的马尔可夫链的问题。使用非线性期望理论，我们用惩罚函数来描述不确定性，可以在时间上代替滤波器向前传播。我们还研究了这种情况下的简单控制问题。