Efficient discretisation of stochastic differential equations
Abstract
The aim of this study is to find a generic method for generating a path of the solution of a given stochastic differential equation which is more efficient than the standard Euler-Maruyama scheme with Gaussian increments. First we characterize the asymptotic distribution of pathwise error in the Euler-Maruyama scheme with a general partition of time interval and then, show that the error is reduced by a factor (d+2)/d when using a partition associated with the hitting times of sphere for the driving d-dimensional Brownian motion. This reduction ratio is the best possible in a symmetric class of partitions. Next we show that a reduction which is close to the best possible is achieved by using the hitting time of a moving sphere which is easier to implement.
Cite
@article{arxiv.1506.05680,
title = {Efficient discretisation of stochastic differential equations},
author = {Masaaki Fukasawa and Jan Obloj},
journal= {arXiv preprint arXiv:1506.05680},
year = {2019}
}