In this paper, we generalize the concept of gamma bridge in the sense that the length will be random, that is, the time to reach the given level is random. The main objective of this paper is to show that certain basic properties of gamma bridges with deterministic length stay true also for gamma bridges with random length. We show that the gamma bridge with random length is a pure jump process and that its jumping times are countable and dense in the random interval bounded by 0 and the random length. Moreover, we prove that this process is a Markov process with respect to its completed natural filtration as well as with respect to the usual augmentation of this filtration, which leads us to conclude that its completed natural filtration is right continuous. Finally, we give its canonical decomposition with respect to the usual augmentation of its natural filtration.

中文翻译：

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随机长度的桥梁：伽马情况

在本文中，我们将伽马桥的概念概括为长度将是随机的，即达到给定水平的时间是随机的。本文的主要目的是证明具有确定长度的伽马桥的某些基本特性对于具有随机长度的伽马桥也是成立的。我们证明了具有随机长度的伽马桥是一个纯跳跃过程，并且它的跳跃次数在以 0 和随机长度为界的随机区间内是可数和密集的。此外，我们证明了这个过程是一个马尔可夫过程，就其完成的自然过滤以及这种过滤的通常增强而言，这使我们得出结论，其完成的自然过滤是正确连续的。最后，