Fractional stochastic differential equation with discontinuous diffusion

ABSTRACT

In this article, we study a class of stochastic differential equations driven by a fractional Brownian motion with H > 1/2 and a discontinuous coefficient in the diffusion. We prove existence and uniqueness for the solution of these equations. This is a first step to define a fractional version of the skew Brownian motion.

KEYWORDS:

• Fractional Brownian motion
• fractional calculus
• pathwise differential equations
• young integral

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G22
• 60H10

Acknowledgments

We would like to thank the anonymous referee for his/her helpful comments, which helped us to improve the presentation of our article. J. Garzón was partially supported by the Project HERMES 16930. Jorge A. León was partially supported by CONACyT grant 220303. S. Torres was partially supported by the Project ECOS - CONICYT C15E05, REDES 150038, MATHAMSUD 16-MATH-03 SIDRE Project and Fondecyt Grant 1171335.