Reflected rough differential equations

Shigeki Aida

Reflected rough differential equations

Probability 2015-04-24 v4

Authors: Shigeki Aida

Abstract

In this paper, we study reflected differential equations driven by continuous paths with finite $p$ -variation ( $1\le p<2$ ) and $p$ -rough paths ( $2\le p<3$ ) on domains in Euclidean spaces whose boundaries may not be smooth. We define reflected rough differential equations and prove the existence of a solution. Also we discuss the relation between the solution to reflected stochastic differential equation and reflected rough differential equation when the driving process is a Brownian motion.

Keywords

reflected backward stochastic differential equations partial differential equations brownian motion

Cite

@article{arxiv.1311.6104,
  title  = {Reflected rough differential equations},
  author = {Shigeki Aida},
  journal= {arXiv preprint arXiv:1311.6104},
  year   = {2015}
}

Comments

This will appear in Stochastic Processes and their applications. doi:10.1016/j.spa.2015.03.008

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