Electronic Journal of Probability

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

Masafumi Hayashi, Arturo Kohatsu, and Go Yuki

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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.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 77, 22 pp.

Accepted: 26 August 2014
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Malliavin Calculus non-smooth drift density function Fourier analysis

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Hayashi, Masafumi; Kohatsu, Arturo; Yuki, Go. Hölder continuity property of the densities of SDEs with singular drift coefficients. Electron. J. Probab. 19 (2014), paper no. 77, 22 pp. doi:10.1214/EJP.v19-2609. https://projecteuclid.org/euclid.ejp/1465065719

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