随机微分方程数值方法的思考

Reflections on the Numerical Scheme to Stochastic Differential Equation

用Euler法求解随机微分方程和关于随机微分方程数值方法的稳定性是当前主要研究方向之一,但其求解结果往往都是方程的离散解,且随着步长的减小,有时离散解并不是更精确。插值法是求连续逼近解的不可或缺的方法,它包括2种方法,即先插值后求一阶、二阶矩和先求矩后插值。文章针对上述2种插值法进行了深入推导,并就其异同点进行分析总结。

Euler method for solving stochastic differential equations and the stability of stochastic differential equations is one of the main research directions, but the solution that the results are often discrete solution of the equation, decreases with the step size, and sometimes the discrete solution is not more accurate. Interpolation is seeking the successive approximation solution of an integral method, which consists of two kinds of methods,interpolated to an order of the second-order moment and seeks first moments after the interpolation. For these two kinds of interpolation in-depth derivation, this paper analyzes and summarizes the similarities and differences.