We study the precise relationship between the subordinate killed and killed subordinate processes in the case of an underlying Hunt process, and show that, under minimal conditions, the former is a subprocess of the latter obtained by killing at a terminal time. Moreover, we also show that the killed subordinate process can be obtained by resurrecting the subordinate killed one at most countably many times.
"On the relationship between subordinate killed and killed subordinate processes." Electron. Commun. Probab. 13 325 - 336, 2008. https://doi.org/10.1214/ECP.v13-1388