A dichotomous property of the total variation of a process with independent increments

We establish a property for the total variation of a cad-lag process with independent increments wich is dichotomous in the sense that only two alternatives are possible. For this purpose we introduce the methods of nonstandard analysis with the study of PII processes in near intervals. Finally we d...

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Autor Principal: Lobo Segura, Jaime
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/186
http://hdl.handle.net/10669/12824
Sumario: We establish a property for the total variation of a cad-lag process with independent increments wich is dichotomous in the sense that only two alternatives are possible. For this purpose we introduce the methods of nonstandard analysis with the study of PII processes in near intervals. Finally we discuss, in the case of continuos processes, an equivalent condition for one of the alternatives of the main theorem.Keywords: total variation of a PII process; Processes with independent increments in near intervals; additive decompositions; regular martingales; continuous shadow theorem; nearby processes.