Abstract
In this paper, we aim to study strong convergence of theta-EM scheme for stochastic differential equations under a local one-sided Lipschitz condition. Since the existence and uniqueness of theta-EM solution cannot be guaranteed under the local one-sided Lipschitz condition, a modified theta-EM scheme is proposed, and strong convergence of the numerical solution to the exact solution is given.
Acknowledgments
The authors would like to thank the associated editor and referees for their helpful comments and suggestions. They would also like to thank Huabin Chen and Ziheng Chen for their useful suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).