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Rough Differential Equations Containing Path-Dependent Bounded Variation Terms

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  • Shigeki Aida

    (The University of Tokyo)

Abstract

We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent stochastic differential equations containing running maximum processes and normal reflection terms. We apply these results to determine the topological support of the solution processes.

Suggested Citation

  • Shigeki Aida, 2024. "Rough Differential Equations Containing Path-Dependent Bounded Variation Terms," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2130-2183, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-024-01319-3
    DOI: 10.1007/s10959-024-01319-3
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    References listed on IDEAS

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    1. Deya, Aurélien & Gubinelli, Massimiliano & Hofmanová, Martina & Tindel, Samy, 2019. "One-dimensional reflected rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3261-3281.
    2. Ledoux, M. & Qian, Z. & Zhang, T., 2002. "Large deviations and support theorem for diffusion processes via rough paths," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 265-283, December.
    3. Aida, Shigeki, 2015. "Reflected rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3570-3595.
    4. Wen Yue & Tusheng Zhang, 2015. "Absolute Continuity of the Laws of Perturbed Diffusion Processes and Perturbed Reflected Diffusion Processes," Journal of Theoretical Probability, Springer, vol. 28(2), pages 587-618, June.
    Full references (including those not matched with items on IDEAS)

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