Non-integrable Stable Approximation by Stein’s Method

We develop Stein’s method for $$\alpha $$ -stable approximation with \in (0,1]$$ , continuing the recent line of research by Xu (Ann Appl Probab 29(1):458–504, 2019) and Chen et al. (J Theor Probab, 2018. https://doi.org/10.1007/s10959-020-01004-1 ) in case (1,2)$$ . The main results include an intrinsic upper bound error a variant Wasserstein distance that involves characterizing differential operators stable distributions application to generalized central limit theorem. Due lack first moment approximating sequence latter result, proof strategy is significantly different from integrable case. rely on fine regularity estimates solution equation established this paper.