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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Banos, David¹  Kruhner, Paul² 

[1] Univ Barcelona, Inst Math, Gran Via Corts Catalanes 585, E-08007 Barcelona, Spain

[2] Vienna Univ Technol, FAM, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

关键词: SDEs;    Regularity of densities;    Irregular drift;    Stochastic control;   

DOI  :  10.1016/j.spa.2016.09.015

来源: Elsevier

【 摘 要 】

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. Holder continuity of the density at any given time is achieved using a different approach than the classical ones in the literature. Namely, the Holder regularity is obtained via a control problem by identifying the equation with the worst global Holder 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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free