Monte Carlo construction of cubature on Wiener space
Probability
2023-05-31 v4 Numerical Analysis
Numerical Analysis
Abstract
In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic differential equations introduced by Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169--198). After giving a brief review of the cubature theory on Wiener space, we show that a cubature formula of general dimension and degree can be obtained through a Monte Carlo sampling and linear programming. This paper also includes an extension of stochastic Tchakaloff's theorem, which technically yields the proof of our primary result.
Keywords
Cite
@article{arxiv.2008.08219,
title = {Monte Carlo construction of cubature on Wiener space},
author = {Satoshi Hayakawa and Ken'ichiro Tanaka},
journal= {arXiv preprint arXiv:2008.08219},
year = {2023}
}
Comments
25 pages