论文标题
为随机微分方程的阳性保留对数Euler-Maruyama类型方案
Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations
论文作者
论文摘要
在本文中，我们提出了一类明确的阳性，以保留具有正溶液的一般随机微分方程的数值方法。也就是说，所有的数值解决方案都是正的。在某些合理的条件下，我们获得了这些方法的收敛性和收敛率。主要困难是获得强大的收敛性和系数为指数增长的随机微分方程的收敛速率。提供了一些数值实验来说明我们方案的理论结果。
In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the numerical solutions are positive. Under some reasonable conditions, we obtain the convergence and the convergence rate results for these methods. The main difficulty is to obtain the strong convergence and the convergence rate for stochastic differential equations whose coefficients are of exponential growth. Some numerical experiments are provided to illustrate the theoretical results for our schemes.
