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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065719

Digital Object Identifier
doi:10.1214/EJP.v19-2609

Mathematical Reviews number (MathSciNet)
MR3256877

Zentralblatt MATH identifier
1310.60081

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

Keywords
Malliavin Calculus non-smooth drift density function Fourier analysis

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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