Brownian motion whose infinitesimal variance changes according to a three-state continuous-time Markov Chain is studied. This Markov Chain can be viewed as a telegraph process with one on state and two off states. We first derive the distribution of occupation time of the on state. Then the result is used to develop a likelihood estimation procedure when the stochastic process at hand is observed at discrete, possibly irregularly spaced time points. The likelihood function is evaluated with the forward algorithm in the general framework of hidden Markov models. The analytic results are confirmed with simulation studies. The estimation procedure is applied to analyze the position data from a mountain lion.

中文翻译：

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具有多个关闭状态的电报过程控制的布朗运动估计

研究了布朗运动，其无限小方差根据三态连续时间马尔可夫链而变化。该马尔可夫链可以看作是具有一个打开状态和两个关闭状态的电报过程。我们首先导出打开状态的占用时间分布。然后，当在离散的，可能不规则的时间点观察到手头的随机过程时，将结果用于制定似然估计程序。在隐马尔可夫模型的一般框架中，使用正演算法评估似然函数。分析结果通过仿真研究得到证实。估计程序用于分析来自山狮的位置数据。