確率微分方程式の数値スキームの誤差における統計的部分

概要

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A lot of discrete approximation schemes in the mean-square sense were proposed for stochastic differential equations. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We already proposed another type of error analysis, that is by means of separating it into two parts(deterministic and stochastic). However, we only investigated the deterministic part, not the stochastic part. In this paper we will examine the stochasric part of global error of numericali solutions for stochastic differential equations, assuming that the normal random numbers are realized ideally. An analysis shows that the simulation for the integral ∫ sdW(s) by 1/2hΔW_i should be carried out carefully. Our results are consistent to Newton's.
日本応用数理学会の論文
1994-06-15