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- Title:
Time Change Representation of Stochastic Integrals
- Document type:
- Zeitschriftenaufsatz
- Author(s):
- Kallsen, J.; A., Shiryaev
- Non-TUM Co-author(s):
- ja
- Cooperation:
- 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
- Journal title:
- Theory of Probability and Its Applications
- Year:
- 2001
- Journal volume:
- 46
- Journal issue:
- 3
- Pages contribution:
- 522-528
- Language:
- en
- Key publication:
- Nein
- Peer reviewed:
- Ja
- International:
- Ja
- Book review:
- Nein
- Commissioned:
- commissioned by government agency
- Professional Journal:
- Nein
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