Simulation studies on time discrete diffusion approximations (Q1095628)

This paper presents and compares the accuracy of numerical results obtained when several methods for simulating the solution to an Îto stochastic differential equation are applied to an example whose exact solution is known. Using 100 blocks with 100 trajectories per block and examining mean-square convergence for three step sizes Euler, second and third order Taylor, and second order derivative free methods, where the order is with respect to mean square convergence, are applied. The same experiment but with different time interval and step sizes is performed to examine mean convergence using Euler, second order Taylor, and second order derivative free methods whose order is with respect to mean convergence.