A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient
Numerical Analysis
2023-12-06 v2 Numerical Analysis
Probability
Abstract
We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted quasi-Milstein scheme we prove -convergence order 3/4. To obtain this result, we prove that under slightly stronger assumptions (but still weaker than anything known before) a related jump-adapted quasi-Milstein scheme has convergence order 3/4 - in a special case even order 1. Order 3/4 is conjectured to be optimal.
Cite
@article{arxiv.2211.08739,
title = {A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient},
author = {Paweł Przybyłowicz and Verena Schwarz and Michaela Szölgyenyi},
journal= {arXiv preprint arXiv:2211.08739},
year = {2023}
}