We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes.

翻译：本文针对一维空间中的复值可积序列，给出了其迭代卷积在任意精度阶下的完整展开。余项估计采用广义高斯界进行严格控制。该结果可应用于概率论中随机游走的研究，以及数值分析中数值格式长时间行为的分析。