Abstract
We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and Hölder continuous drift has a Hölder continuous density function. This result complements recent results of Fournier–Printems (Bernoulli 16(2):343–360, 2010), where the density is shown to exist if both coefficients are Hölder continuous, and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion.
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