Order-preserving strong schemes for SDEs with locally Lipschitz coefficients
Provides numerical schemes for SDEs with locally Lipschitz coefficients, addressing a known bottleneck in stochastic numerics.
The paper introduces explicit balanced schemes for SDEs with superlinearly growing coefficients, achieving order-half (Euler) and order-one (Milstein) mean-square convergence, with order-one for Euler under additive noise.
We introduce a class of explicit balanced schemes for stochastic differential equations with coefficients of superlinearly growth satisfying a global monotone condition. The first scheme is a balanced Euler scheme and is of order half in the mean-square sense whereas it is of order one under additive noise. The second scheme is a balanced Milstein scheme, which is of order one in the mean-square sense. Some numerical results are presented.