On explicit order 1.5 approximations with varying coefficients: the case of super-linear diffusion coefficients
Probability
2018-11-07 v2 Numerical Analysis
Abstract
A conjecture appears in \cite{milsteinscheme}, in the form of a remark, where it is stated that it is possible to construct, in a specified way, any high order explicit numerical schemes to approximate the solutions of SDEs with superlinear coefficients. We answer this conjecture affirmatively for the case of order 1.5 approximations and show that the suggested methodology works. Moreover, we explore the case of having H\"{o}lder continuous derivatives for the diffusion coefficients.
Keywords
Cite
@article{arxiv.1707.05086,
title = {On explicit order 1.5 approximations with varying coefficients: the case of super-linear diffusion coefficients},
author = {Sotirios Sabanis and Ying Zhang},
journal= {arXiv preprint arXiv:1707.05086},
year = {2018}
}