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Local Skorokhod topology on the space of cadlag processes. (English) Zbl 1414.60003

Summary: We modify the global Skorokhod topology, on the space of cadlag paths, by localising with respect to space variable, in order to include the eventual explosions. The tightness of families of probability measures on the paths space endowed with this local Skorokhod topology is studied and a characterization of Aldous type is obtained. The local and global Skorokhod topologies are compared by using a time change transformation.

MSC:

60B10 Convergence of probability measures
54H99 Connections of general topology with other structures, applications
60J75 Jump processes (MSC2010)
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