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Time-Changed Local Martingales Under Signed Measures

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  • Sakrani Samia

    (University of 8 Mai 1945)

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 $$(\varOmega ,{\mathcal {F}}, {{P}}),$$ ( Ω , F , P ) , such that $$\left| Q\right| $$ Q and P are equivalent. In the first part of the paper, we generalize the results of stochastic calculus in Beghdadi-Sakrani (Séminaire de probabilités 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.

Suggested Citation

  • Sakrani Samia, 2021. "Time-Changed Local Martingales Under Signed Measures," Journal of Theoretical Probability, Springer, vol. 34(2), pages 644-659, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00994-2
    DOI: 10.1007/s10959-020-00994-2
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    References listed on IDEAS

    as
    1. Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 917-938, June.
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