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arXiv · 1506.05680

Efficient discretisation of stochastic differential equations

Masaaki Fukasawa·Jan Obloj
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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.

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Masaaki Fukasawa, Jan Obloj. 2015-06-18. Efficient discretisation of stochastic differential equations. https://doi.org/10.1080/17442508.2019.1666131

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