论文标题
使用时间更改方法的一维随机微分方程的新离散方案
A New Discretization Scheme for One Dimensional Stochastic Differential Equations Using Time Change Method
论文作者
论文摘要
我们为一维随机微分方程（SDE）提出了一种新的数值方法。该方法的主要思想是基于随着时间变化的Brownian运动的SDE弱解的表示，其历史可以追溯到Doeblin（1940）。如果扩散系数有界，并且$β$-Hölder连续$ 0 <β\ leq 1 $连续，我们提供了强收敛的速率。我们方法的一个优点是我们近似弱解决方案，这使我们能够在没有强大解决方案的情况下对待SDE。我们的方案是第一个实现$ 0 <β<1/2 $的强大收敛性的计划。
We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this method is based on a representation of a weak solution of a SDE with a time changed Brownian motion, dated back to Doeblin (1940). In cases where the diffusion coefficient is bounded and $β$-Hölder continuous with $0 < β\leq 1$, we provide the rate of strong convergence. An advantage of our approach is that we approximate the weak solution, which enables us to treat a SDE with no strong solution. Our scheme is the first to achieve the strong convergence for the case $0 < β< 1/2$.
