Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients
Copyright policy )Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients
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 Lebesgue density of that process at any given time is achieved using a different approach than the classical ones in the literature. Namely, the Hölder regularity of the densities is obtained via a control problem by identifying the stochastic differential equation with the worst global Hölder constant. Then we generalise our findings to a larger class of diffusion coefficients. The novelty of this method is that it is not based on a variational calculus and it is suitable for non-Markovian processes.
14 pages
- TU Wien Austria
- University of Barcelona Spain
- WU Austria
60H10, 49N60, regularity, densities, Probability (math.PR), Regularity of solutions in optimal control, FOS: Mathematics, stochastic control, irregular drift, stochastic differential equations, Mathematics - Probability, Stochastic ordinary differential equations (aspects of stochastic analysis)
60H10, 49N60, regularity, densities, Probability (math.PR), Regularity of solutions in optimal control, FOS: Mathematics, stochastic control, irregular drift, stochastic differential equations, Mathematics - Probability, Stochastic ordinary differential equations (aspects of stochastic analysis)
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