Projected Euler method for stochastic delay differential equation under a global monotonicity condition
Numerical Analysis
2018-10-24 v1
Abstract
This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalized the idea of C-stability and B-consistency given by Beyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay. Moreover, the method is proved to be convergent with order in a succinct way. Finally, some numerical examples are included to illustrate the obtained theoretical results.
Cite
@article{arxiv.1810.09647,
title = {Projected Euler method for stochastic delay differential equation under a global monotonicity condition},
author = {Min Li and Chengming Huang},
journal= {arXiv preprint arXiv:1810.09647},
year = {2018}
}