an:06734594
Zbl 1367.60064
Ba??os, David; Kr??hner, Paul
H??lder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients
EN
Stochastic Processes Appl. 127, No. 6, 1785-1799 (2017).
00367097
2017
j
60H10 49N60
stochastic differential equations; densities; regularity; irregular drift; stochastic control
Summary: 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. H??lder continuity of the density at any given time is achieved using a different approach than the classical ones in the literature. Namely, the H??lder regularity is obtained via a control problem by identifying the equation with the worst global H??lder 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.