Hölder continuity property of the densities of SDEs with singular drift coefficients

Masafumi Hayashi (University of the Ryukyus and Japan Science and Technology Agency)
Arturo Higa Kohatsu (Ritsumeikan University and Japan Science and Technology Agency)
Go Yuki (Ritsumeikan University and Japan Science and Technology Agency)

Abstract


We prove that the solution of stochastic differential equations with deterministic diffusion coefficient admits a Hölder continuous density via a condition on the integrability of the Fourier transform of the drift coefficient. In our result, the integrability is an important factor to determine the order of Hölder continuity of the density. Explicit examples and some applications are given.

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Pages: 1-22

Publication Date: August 26, 2014

DOI: 10.1214/EJP.v19-2609

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