一类标量随机微分方程的一阶显式保正格式分析
Analysis of a first-order explicit positivity preserving scheme for a class of scalar SDEs
AI总结：
针对一类几乎必然有正解的标量伊藤随机微分方程，提出并分析一种一阶显式保正数值格式，证明其一阶强收敛性，还展示了如何将该格式适配到具有正解的斯特拉托诺维奇随机微分方程。
AI中文摘要：
针对一类几乎必然有正解的标量伊藤随机微分方程，本文提出并分析一种一阶数值格式。我们构造了一种新的显式数值格式，使得无论时间步长如何选取，数值解都能保证几乎必然为正。本文的主要结果是该保正格式的一阶强收敛性，这一点通过数值实验得到了说明，且已被严格证明。本文还展示了如何将该格式及结果适配到具有正解的斯特拉托诺维奇随机微分方程上。
英文摘要：
We propose and analyze a first-order numerical scheme for a class of scalar Itô stochastic differential equations with almost surely positive solutions. We construct a new explicit numerical scheme, such that for any choice of the time-step size, the numerical solution is guaranteed to remain almost surely positive. The main result of this article is the first-order strong convergence of the proposed positivity preserving scheme, which is illustrated with numerical experiments and proved rigorously. It is also shown how to adapt the scheme and the results to Stratonovich stochastic differential equations with positive solutions.
