For given two standard processes with no positive jumps, we construct, using excursion theory, a Markov process whose positive and negative motions have the same law as the two processes. The resulting process is a generalization of Kyprianou–Loeffen’s refracted Lévy processes. We discuss approximation problem for our refracted processes coming from Lévy processes by removing small jumps and taking the limit as the removal level tends to zero. We also discuss conditions for refracted processes to have dual processes.

中文翻译：

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折射过程的逼近和对偶问题

对于给定的两个没有正跳的标准过程，我们使用偏移理论构造了一个马尔可夫过程，该过程的正负运动与这两个过程具有相同的规律。结果过程是Kyprianou-Loeffen的折射Lévy过程的推广。我们讨论了来自Lévy过程的折射过程的近似问题，方法是消除微小的跳跃，并在消除水平趋于零时采用极限。我们还将讨论折射过程具有双重过程的条件。