SDEs with constraints driven by processes with bounded p-variation

TL;DR

This paper investigates the existence, uniqueness, and approximation of constrained stochastic differential equations driven by processes with bounded p-variation, introducing new Lipschitz estimates for the Skorokhod problem and applying them to fractional SDEs.

Contribution

It provides novel Lipschitz continuity estimates for the Skorokhod problem in p-variation norm, enabling analysis of SDEs with constraints driven by processes with bounded p-variation.

Findings

Established existence and uniqueness results for constrained SDEs with bounded p-variation drivers.

Developed new Lipschitz estimates for the Skorokhod problem in p-variation norm.

Applied the theoretical results to fractional SDEs with constraints.

Abstract

We study the existence, uniqueness and approximation of solutions of stochastic differential equations with constraints driven by processes with bounded p-variation. Our main tool are new estimates showing Lipschitz continuity of the deterministic Skorokhod problem in p-variation norm. Applications to fractional SDEs with constraints are given.