In this paper, our first goal is to rigorously define a Lévy process pinned at random time. Our second task is to establish the Markov property with respect to its completed natural filtration and thus with respect to the usual augmentation of the latter. The resulting conclusion is the right-continuity of completed natural filtration. Certain examples of such process are considered.

中文翻译：

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在随机时间固定的Lévy过程中

在本文中，我们的首要目标是严格定义随机固定的Lévy流程。我们的第二个任务是就其完成的自然过滤并因此相对于后者的通常增强而言，建立马尔可夫性质。得出的结论是完全自然过滤的右连续性。考虑这种过程的某些例子。