On the Skorokhod topology
نویسنده
چکیده
Let E be a completely regular topological space. Mitoma [9 ], extending the classical case E = R 1, has recently introduced the Skorokhod topology on the space D( [0, 1 ] : E). This topology is investigated in detail. We find families of continuous functions which generate the topology, examine the structure of the Borel and Baire a-algebras of D( [0, 1 ] : E) and prove tightness criteria for E-valued stochastic processes. Extensions to D(R + : E) are also given. RESUME. Soit E un espace topologique completement regulier. Etendant le cas classique, Mitoma [9] ] vient d’introduire recemment la topologie de Skorokhod sur l’espace D( [0, 1 ] : E). Nous examinons en detail cette topologie, donnons des families d’applications continues engendrant la topologie : nous etudions la structure des tribus de Borel et de Baire de D( [0, 1 ] : E) et demontrons des criteres de tension pour les processus stochastiques. Nous terminons par des extensions a D(R + : E).
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