Numerical analysis of the balanced methods for stochastic Volterra integro-differential equations

This thesis mainly proves the strong convergence and the stability in mean-square sense of the implicit balanced methods for the stochastic Volterra integro-differential equations. The balanced implicit methods are proved to give strong convergence rate of 1/2. Furthermore, the paper shows that the balanced implicit methods are stable in mean-square sense with the fully small stepsize. The theoretical results are verified by numerical experiments.