Some Issues in Discrete Approximate Solution for Stochastic Differential Equations(Workshop on Stochastic Numerics)

Abstract An evaluation method for numerical schemes of stochastic differential equations is treated. Discussing the source of errors in the discrete numerical solution, we highlight the effect of pseudo-random numbers upon the numerical solution, and point out the significance of the independencies of the series of them required in the numerical schemes. To discriminate the stochastic and deterministic parts in the errors more clearly, we propose a new two-dimensional linear test equation of multiplicative type whose analytical solution can be obtained readily. Our results are illustrated through some numerical examples.