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Titel:

Time Change Representation of Stochastic Integrals

Dokumenttyp:
Zeitschriftenaufsatz
Autor(en):
Kallsen, J.; A., Shiryaev
Nicht-TUM Koautoren:
ja
Kooperation:
international
Abstract:
By the Dambis-Dubins-Schwarz theorem, any stochastic integral M of Brownian motion can be written as a time-changed Brownian motion. Rosinski and Woyczynski (1986) and Kallenberg (1992) showed that in this statement Brownian motion can be replaced with (symmetric) α -stable Lévy motion. Using the cumulant process of a semimartingale, we give new short proofs. Moreover, we show that the statement cannot be extended to any other Lévy processes.
Intellectual Contribution:
Discipline-based Research
Zeitschriftentitel:
Theory of Probability and Its Applications
Jahr:
2001
Band / Volume:
46
Heft / Issue:
3
Seitenangaben Beitrag:
522-528
Sprache:
en
Key publication:
Nein
Peer reviewed:
Ja
International:
Ja
Book review:
Nein
commissioned:
commissioned by government agency
Professional Journal:
Nein
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