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Positivity of the Density for Rough Differential Equations

Author

Listed:
  • Yuzuru Inahama

    (Kyushu University)

  • Bin Pei

    (Northwestern Polytechnical University)

Abstract

Due to recent developments of Malliavin calculus for rough differential equations, it is now known that, under natural assumptions, the law of a unique solution at a fixed time has a smooth density function. Therefore, it is quite natural to ask whether or when the density is strictly positive. In this paper we study this problem from the viewpoint of Aida–Kusuoka–Stroock’s general theory.

Suggested Citation

  • Yuzuru Inahama & Bin Pei, 2022. "Positivity of the Density for Rough Differential Equations," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1863-1877, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01116-2
    DOI: 10.1007/s10959-021-01116-2
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    References listed on IDEAS

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    1. Benjamin Gess & Cheng Ouyang & Samy Tindel, 2020. "Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths," Journal of Theoretical Probability, Springer, vol. 33(2), pages 611-648, June.
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