Cox-Ingersoll-Ross过程全截断Euler逼近的1/2阶强收敛性
Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process
摘要：
研究了Cox-Ingersoll-Ross过程的全截断Euler格式在边界点零点不可达区域的收敛性。在一定的模型参数条件下（确切地说，当Feller比大于3时），我们证明了格式在$L^{p}$中强1/2阶收敛到精确解.这与全局Lipschitz系数的随机微分方程的欧拉近似的最优强收敛速度是一致的，尽管Cox-Ingersoll-Ross模型中的扩散系数不是Lipschitz。
英文摘要：
We study convergence properties of the full truncation Euler scheme for the Cox-Ingersoll-Ross process in the regime where the boundary point zero is inaccessible. Under some conditions on the model parameters (precisely, when the Feller ratio is greater than three), we establish the strong order 1/2 convergence in $L^{p}$ of the scheme to the exact solution. This is consistent with the optimal rate of strong convergence for Euler approximations of stochastic differential equations with globally Lipschitz coefficients, despite the fact that the diffusion coefficient in the Cox-Ingersoll-Ross model is not Lipschitz.
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