A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications

@article{Tretyakov2013AFM,
title={A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications},
author={Michael V. Tretyakov and Zhongqiang Zhang},
journal={SIAM J. Numerical Analysis},
year={2013},
volume={51},
pages={3135-3162}
}

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDEs) in which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The theorem is illustrated on a number of particular numerical methods, including a special balanced scheme and fully implicit methods. The proposed special balanced scheme is explicit and its mean-square order of convergence is 1/2. Some numerical tests are… CONTINUE READING