论文标题
连续无时间跳过下向下马尔可夫链的波动理论，并应用于移民的分支过程
Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration
论文作者
论文摘要
我们开发了一种新的方法，用于连续无时间跳过马尔可夫链的波动理论，从而扩展了Choi和Patie [5]的最新工作，用于离散的无时间跳过Markov链。作为主要应用程序，我们使用它来得出一组全套波动身份，以使马尔可夫分支过程中的有限或无限间隔进行移民，从而发现了这个经典的连续时间马尔可夫连锁店的新结果。该理论还使我们能够以简单的方式恢复自动向下的复合泊松工艺的波动身份。
We develop a new methodology for the fluctuation theory of continuous-time skip-free Markov chains, extending the recent work of Choi and Patie [5] for discrete-time skip-free Markov chains. As the main application we use it to derive a full set of fluctuation identities regarding exiting a finite or infinite interval for Markov branching processes with immigration, thereby uncovering many new results for this classical family of continuous-time Markov chains. The theory also allows us to recover in a simple manner fluctuation identities for skip-free downward compound Poisson processes.
