Reflected rough differential equations

Shigeki Aida

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, we study reflected differential equations driven by continuous paths with finite p-variation (1≥<2) and p-rough paths (2≥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.

Original languageEnglish
Pages (from-to)3570-3595
Number of pages26
JournalStochastic Processes and their Applications
Volume125
Issue number9
DOIs
Publication statusPublished - 2015 Jul 28

Keywords

  • Reflected stochastic differential equation
  • Rough path
  • Skorohod equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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