Details

Autor(en) / Beteiligte

• Caballero, M. E.
• Chaumont, L.

Titel

Weak Convergence of Positive Self-Similar Markov Processes and Overshoots of Lévy Processes

Ist Teil von

• The Annals of probability, 2006-05, Vol.34 (3), p.1012-1034

Ort / Verlag

Hayward: Institute of Mathematical Statistics

Erscheinungsjahr

2006

Link zum Volltext

Quelle

Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals

Beschreibungen/Notizen

• Using Lamperti's relationship between Lévy processes and positive self-similar Markov processes (pssMp), we study the weak convergence of the law${\Bbb P}_{x}$of a pssMp starting at x > 0, in the Skorohod space of càdlàg paths, when x tends to 0. To do so, we first give conditions which allow us to construct a càdlàg Markov process X⁽⁰⁾, starting from 0, which stays positive and verifies the scaling property. Then we establish necessary and sufficient conditions for the laws${\Bbb P}_{x}$to converge weakly to the law of X⁽⁰⁾ as x goes to 0. In particular, this answers a question raised by Lamperti [Z. Wahrsch. Verw. Gebiete 22 (1972) 205-225] about the Feller property for pssMp at x = 0.