一维非对称α-稳定莱维运动生成元的有限差分方法
Finite Difference Methods for the generator of 1D asymmetric alpha-stable Lévy motions
AI总结：
本文提出几种有限差分方法用于计算一维非对称α-稳定莱维运动的生成元，通过将操作符转换为谱空间中的乘法子，采用离散卷积形式，通过选择系数近似精确乘子，讨论了精度及优缺点，为实际问题提供指导。
摘要：
本文提出几种有限差分方法用于计算一维非对称α-稳定莱维运动的生成元，基于操作符在谱空间中成为乘法子的事实。这些方法通常以离散卷积形式出现，卷积中的系数（或权重）被选择以在适当变换后近似精确乘子。讨论了精度及相关的优缺点，为实际问题提供指导，例如随机过程的均退出时间计算。
英文摘要：
Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric $α$-stable Lévy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general form of a discrete convolution, and the coefficients (or the weights) in the convolution are chosen to approximate the exact multiplier after appropriate transform. The accuracy and the associated advantages/disadvantages are also discussed, providing some guidance on the choice of the right scheme for practical problems, like in the calculation of mean exit time for random processes governed by general asymmetric $α$-stable motions.
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