论文标题
用于夹层过程的漂移 - 毫无疑问的欧拉计划由Hölder噪声驱动
Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises
论文作者
论文摘要
在本文中，我们分析了一类随机微分方程的漂移渐变（或向后）的欧拉数值方案，这些方程是由任意$λ$-Hölder连续过程驱动的无界漂移，$λ\ in（0,1）$。我们证明，在噪声的Hölder常数的一些温和的时刻假设下，$ l^r（ω; l^\ infty（[0，t]））$ - 收敛速率等于$λ$。为了举例说明，我们考虑了广义的Cox-Ingersoll-Ross和Tsallis-stariolo-borland模型的数值方案。结果通过模拟说明。
In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary $λ$-Hölder continuous process, $λ\in(0,1)$. We prove that, under some mild moment assumptions on the Hölder constant of the noise, the $L^r(Ω;L^\infty([0,T]))$-rate of convergence is equal to $λ$. To exemplify, we consider numerical schemes for the generalized Cox--Ingersoll-Ross and Tsallis--Stariolo--Borland models. The results are illustrated by simulations.
