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Itô’s formula for flows of measures on semimartingales

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  • Guo, Xin
  • Pham, Huyên
  • Wei, Xiaoli

Abstract

We establish Itô’s formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô’s formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques.

Suggested Citation

  • Guo, Xin & Pham, Huyên & Wei, Xiaoli, 2023. "Itô’s formula for flows of measures on semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 350-390.
    • Handle: RePEc:eee:spapps:v:159:y:2023:i:c:p:350-390
    DOI: 10.1016/j.spa.2023.02.004
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    References listed on IDEAS

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    1. Bensoussan, A. & Frehse, J. & Yam, S.C.P., 2017. "On the interpretation of the Master Equation," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2093-2137.
    2. Medvegyev, Peter, 2007. "Stochastic Integration Theory," OUP Catalogue, Oxford University Press, number 9780199215256.
    3. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.
    4. N. C. Framstad & B. Øksendal & A. Sulem, 2004. "Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 77-98, April.
    5. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.
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