Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients
Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients
复制标题
DOI：
10.1007/s10208-011-9101-9
复制
发表时间：
2009-12
影响因子：
3
通讯作者：
Martin Hutzenthaler;Arnulf Jentzen
中科院分区：
文献类型：
--
作者：
Martin Hutzenthaler;Arnulf Jentzen
随机微分方程通常用蒙特卡罗-欧拉方法模拟。在随机微分方程具有全局Lipschitz连续系数的情况下，这种方法的收敛性得到了很好的理解。然而，超线性增长系数的重要情况仍然是一个悬而未决的问题。主要的困难是数值上的弱收敛在许多超线性增长系数的情况下不能成立。本文克服了这一困难，对一类漂移函数最多有多项式增长的一维随机微分方程，建立了蒙特卡罗-欧拉方法的收敛性。
Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. However, the important case of superlinearly growing coefficients has remained an open question. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations whose drift functions have at most polynomial growth.