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Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients

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  • Baños, David
  • Krühner, Paul

Abstract

We consider a process given as the solution of a one-dimensional stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Hölder continuity of the density at any given time is achieved using a different approach than the classical ones in the literature. Namely, the Hölder regularity is obtained via a control problem by identifying the equation with the worst global Hölder constant. Then we generalise our findings to a larger class of diffusions. The novelty of this method is that it is not based on a variational calculus and it is suitable for non-Markovian processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:6:p:1785-1799
    DOI: 10.1016/j.spa.2016.09.015
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    References listed on IDEAS

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    1. 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.
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