Consider a non-explosive positive Feller process with no negative jumps. It is shown in this note that when infinity is an entrance boundary, in the sense that the entrance times of the process remain bounded when the initial value tends to infinity, the process admits a Feller extension on the compactified state space $[0,\infty]$. Moreover, when started from infinity, the extended Markov process on $[0,\infty]$ leaves infinity instantaneously and stays finite, almost-surely. Arguments are adapted from a proof given by O. Kallenberg for diffusions. We also show that the process started from $x$ converges weakly towards that started from infinity in the Skorokhod space, when $x$ goes to infinity.

中文翻译：

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在无穷远的 Feller 过程的入口处，没有负跳跃

考虑一个没有负跳跃的非爆炸正 Feller 过程。在这个注解中表明，当无穷大是入口边界时，从这个意义上说，当初始值趋于无穷大时，过程的入口时间保持有界，过程在紧致状态空间 $[0,\ infty]$。此外，当从无穷大开始时，$[0,\infty]$ 上的扩展马尔可夫过程会立即离开无穷大并保持有限，几乎可以肯定。参数改编自 O. Kallenberg 为扩散给出的证明。我们还表明，当 $x$ 趋于无穷大时，从 $x$ 开始的过程在 Skorokhod 空间中向从无穷大开始的过程弱收敛。