A unified approach to Stein’s method for stable distributions

In this article, we first review the connection between Lévy processes and infinitely divisible random variables, discuss classification of distributions. Next, establish a Stein identity for an variable via Lévy-Khintchine representation characteristic function. particular, unify identities α-stable available in existing literature. derive solutions equations its regularity estimates. Further, error bounds approximations, also obtain rates convergence results Wasserstein-δ,δ<α α∈(0,1) Wasserstein-type distances α∈(1,2). Finally, compare these with