From rough path estimates to multilevel Monte Carlo
Probability
2016-06-20 v3
Abstract
New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations driven by Gaussian noise in the aforementioned sense. Our focus lies on numerical implementations, and more specifically on the saving possible via multilevel methods. Our analysis relies on a subtle combination of pathwise estimates, Gaussian concentration, and multilevel ideas. Numerical examples are given which both illustrate and confirm our findings.
Cite
@article{arxiv.1305.5779,
title = {From rough path estimates to multilevel Monte Carlo},
author = {Christian Bayer and Peter K. Friz and Sebastian Riedel and John Schoenmakers},
journal= {arXiv preprint arXiv:1305.5779},
year = {2016}
}
Comments
34 pages