抛物随机微分方程的多水平Monte Carlo法

Multilevel Monte Carlo Method for Parabolic Stochastic Differential Equations

在热传导、化学物质扩散的问题中,常出现带有随机系数的抛物偏微分方程,而求这些随机抛物微分方程的解析解非常困难,因此考虑其数值近似。本文用多水平Monte Carlo法和有限差分法相结合来求解抛物随机问题的数值解,与传统的Monte Carlo法相比,它的渐近成本显著降低,计算速度显著提高,数值算例检验了该方法的高效性。

Parabolic partial differential equations with stochastic coefficients often appear in heat conduction or diffusion of chemical substances.It is very difficult to find the analytical solutions of these stochastic parabolic differential equations,so the numerical approximation is considered.In this paper,the multilevel Monte Carlo method and the finite difference method are combined to solve the numerical solution of parabolic stochastic problems.Compared with the traditional Monte Carlo method,the asymptotic cost of the method is significantly reduced and the computational speed is significantly increased.The efficiency of the method is verified by numerical examples.