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

David Baños and Paul Krühner

Stochastic Processes and their Applications, 2017, vol. 127, issue 6, 1785-1799

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.

Keywords: SDEs; Regularity of densities; Irregular drift; Stochastic control (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:6:p:1785-1799

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DOI: 10.1016/j.spa.2016.09.015

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