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Estimates for the density of functionals of SDEs with irregular drift

Author

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  • Kohatsu-Higa, Arturo
  • Makhlouf, Azmi

Abstract

We obtain upper and lower bounds for the density of a functional of a diffusion whose drift is bounded and measurable. The argument consists of using Girsanov’s theorem together with an Itô–Taylor expansion of the change of measure. One then applies Malliavin calculus techniques in a non-trivial manner so as to avoid the irregularity of the drift. An integration by parts formula for this set-up is obtained.

Suggested Citation

  • Kohatsu-Higa, Arturo & Makhlouf, Azmi, 2013. "Estimates for the density of functionals of SDEs with irregular drift," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1716-1728.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:5:p:1716-1728
    DOI: 10.1016/j.spa.2013.01.006
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    Cited by:

    1. Baños, David & Krühner, Paul, 2017. "Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1785-1799.
    2. 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.
    3. Nguyen, Tien Dung, 2018. "Tail estimates for exponential functionals and applications to SDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4154-4170.

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