Path dependent equations driven by Hölder processes

Abstract

This article investigates existence results for path-dependent differential equations driven by a Hölder function where the integrals are understood in the Young sense. The two main results are proved via an application of Schauder theorem and the vector field is allowed to be unbounded. The Hölder function is typically the trajectory of a stochastic process.

Keywords:

• Young integration
• path-dependent
• differential equations

Mathematics Subject Classification:

• 60G22
• 60H05
• 60H22

Acknowledgments

The authors would like to thank the Referee and the Editors for their comments. The first named author was supported by the (Brazilian) National Council for Scientific and Technological Development (CNPq), under grant Nr. 232925/2014-3. Part of the work was done during a visit of the second author to the University of Bielefeld, SFB 701. He is grateful to Prof. Michael Röckner for the kind invitation.