First time to exit of a continuous Itô process: General moment estimates and L1 -convergence rate for discrete time approximations
First time to exit of a continuous Itô process: General moment estimates and L1 -convergence rate for discrete time approximations
复制标题
首次退出连续 Itô 过程：离散时间近似的一般矩估计和 L1 收敛率
作者：
B. Bouchard;S. Geiss;E. Gobet
我们根据到边界的距离，建立了一般It\^{o}过程的离散和连续退出时间的一般矩估计。这些估计作为中间步骤，以获得在网格上计算的离散对应的连续退出时间的近似的强收敛结果。特别地，我们证明了扩散的欧拉格式的离散退出时间收敛于与网格大小有关的1/2阶的L_1范数。
We establish general moment estimates for the discrete and continuous exit times of a general It\^{o} process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the $L_1$ norm with an order $1/2$ with respect to the mesh size.
影响因子：
2.7
作者：
Giles, Michael B.
通讯作者：
Giles, Michael B.