Abstract: We discussed the convergence and stability by using the fully implicit numerical method—balanced methods for a class of stochastic variable delay differential equations. Firstly, we proved that the numerical solution of the equation converged to the exact solution in 1/2 order mean-square. Secondly, we proved that the method could keep the mean-square stability of the analytical solution. Finally, the correctness of the theoretical results was verified by numerical experiments.

Key words: stochastic variable delay differential equation, balanced method, mean-square convergence, mean-square stability