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Time-Changed Local Martingales Under Signed Measures
- Source :
- Journal of Theoretical Probability. 34:644-659
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we use stochastic integration in the framework of signed measures, together with the technique of time changes. Let Q be a bounded non-null signed measure on $$(\varOmega ,{\mathcal {F}}, {{P}}),$$ such that $$\left| Q\right| $$ and P are equivalent. In the first part of the paper, we generalize the results of stochastic calculus in Beghdadi-Sakrani (Seminaire de probabilites XXXVI, Springer, 2003) to Q-local martingales and we give some examples. In the second part, we prove that the class of Q-semimartingales is invariant under time changes. We establish the famous formulas of time-changed local martingales as well as the representation of a Q-local martingale as a time-changed Brownian motion.
- Subjects :
- Statistics and Probability
Discrete mathematics
General Mathematics
Signed measure
010102 general mathematics
Stochastic calculus
01 natural sciences
Time changes
Stochastic integration
010104 statistics & probability
Mathematics::Probability
Bounded function
0101 mathematics
Statistics, Probability and Uncertainty
Martingale (probability theory)
Brownian motion
Mathematics
Subjects
Details
- ISSN :
- 15729230 and 08949840
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- Journal of Theoretical Probability
- Accession number :
- edsair.doi...........d3d42d069ef3773fc9f6c8fdcb9cd347