论文标题
刚性的泰勒方案的半尺寸泰勒方案
Semi-implicit Taylor schemes for stiff rough differential equations
论文作者
论文摘要
我们研究了一类半图像的泰勒型数值方法，这些方法易于实施，并且设计用于解决由一般粗糙噪声驱动的多维随机微分方程，例如小部分布朗运动。在乘法噪声情况下，该方程在T. 〜lyons的意义上被理解为一个粗糙的微分方程。我们关注的方程式可能是无限的，仅满足单方面的Lipschitz条件。我们证明了这些方法的适合性，提供了完整的分析并推断出它们的收敛速度。数值实验表明，我们的方案在由小数布朗运动驱动的僵硬的粗糙随机微分方程中特别有用。
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the multiplicative noise case, the equation is understood as a rough differential equation in the sense of T.~Lyons. We focus on equations for which the drift coefficient may be unbounded and satisfies a one-sided Lipschitz condition only. We prove well-posedness of the methods, provide a full analysis, and deduce their convergence rate. Numerical experiments show that our schemes are particularly useful in the case of stiff rough stochastic differential equations driven by a fractional Brownian motion.
