Adaptive Euler-Maruyama Method for SDEs with Non-globally Lipschitz Drift: Part I, Finite Time Interval
Numerical Analysis
2016-09-27 v1
Abstract
This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with a drift which is not globally Lipschitz. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Furthermore, the order of strong convergence is the same as usual, i.e. order one-half for SDEs with a non-uniform globally Lipschitz volatility, and order one for Langevin SDEs with unit volatility and a drift with sufficient smoothness. The analysis is supported by numerical experiments for a variety of SDEs.
Cite
@article{arxiv.1609.08101,
title = {Adaptive Euler-Maruyama Method for SDEs with Non-globally Lipschitz Drift: Part I, Finite Time Interval},
author = {Wei Fang and Michael Bryce Giles},
journal= {arXiv preprint arXiv:1609.08101},
year = {2016}
}