一类随机微分方程的显式保域数值格式
Explicit domain preserving numerical schemes for a class of stochastic differential equations
浏览论文内容
中文总结 AI 辅助
针对几乎必然保持任意维超立方体的随机微分方程，本文提出通用显式保域数值格式，证明其强阶1/2、弱阶1的收敛性，构造变体实现强阶1，通过实验验证结果。
中文摘要 AI 辅助
本文针对一类随机微分方程系统构造并分析了几乎必然保持任意维超立方体的数值格式。我们提出了一类新的通用显式格式，该格式在任意时间步长下，数值解均取值于该超立方体中。我们证明了这类通用保域数值格式的强收敛与弱收敛结果，其强阶通常为1/2，弱阶通常为1。我们还构造了该格式的一个变体，当随机微分方程由一维布朗运动驱动时，该变体可达到强阶1。数值实验验证了这些收敛结果。
英文摘要
We construct and analyze numerical schemes for systems of stochastic differential equations, which preserve almost surely a given hypercube of arbitrary dimension. We propose a new general class of explicit schemes, such that for any choice of the time-step size the numerical solution takes values in the hypercube. We prove strong and weak convergence results for this general class of domain preserving numerical schemes, with strong order $1/2$ and weak order $1$ in general. We also construct a variant of the scheme which achieves strong order $1$ when the stochastic differential equation is driven by a one-dimensional Brownian motion. The convergence results are illustrated with numerical experiments.
