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Local Hölder Continuity Property of the Densities of Solutions of SDEs with Singular Coefficients

Author

Listed:
  • Masafumi Hayashi

    (University of the Ryukyus, and Japan Science and Technology Agency)

  • Arturo Kohatsu-Higa

    (Ritsumeikan University and Japan Science and Technology Agency)

  • Gô Yûki

    (Ritsumeikan University and Japan Science and Technology Agency)

Abstract

We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and Hölder continuous drift has a Hölder continuous density function. This result complements recent results of Fournier–Printems (Bernoulli 16(2):343–360, 2010), where the density is shown to exist if both coefficients are Hölder continuous, and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion.

Suggested Citation

  • Masafumi Hayashi & Arturo Kohatsu-Higa & Gô Yûki, 2013. "Local Hölder Continuity Property of the Densities of Solutions of SDEs with Singular Coefficients," Journal of Theoretical Probability, Springer, vol. 26(4), pages 1117-1134, December.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:4:d:10.1007_s10959-012-0430-7
    DOI: 10.1007/s10959-012-0430-7
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    Cited by:

    1. Tomonori Nakatsu, 2019. "Some Properties of Density Functions on Maxima of Solutions to One-Dimensional Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1746-1779, December.

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