Local Skorokhod topology on the space of cadlag processes

Mihai Gradinaru (1) , Tristan Haugomat (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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. A number of results in the paper should play an important role when studying Lévy-type processes with unbounded coefficients by martingale problem approach.

Mots clés: cadlag processes; explosion time; local Skorokhod topology; Aldous tightness criterion; time change transformation

Domaines: Probabilités [math.PR]; Topologie générale [math.GN]

Mihai Gradinaru, Tristan Haugomat. Local Skorokhod topology on the space of cadlag processes. 2017. ⟨hal-01537750v1⟩