Quantitative Generalized Central Limit Theorems with Self-Decomposable and Symmetric Stable Limiting Laws
This work provides new stability estimates for centered non-degenerate self-decomposable probability measures on Rd with finite second moment and for non-degenerate symmetric α-stable probability measures on Rd with α ∈ (1, 2). The proofs rely on Stein's method, closed forms techniques, and weighted Poincaré-type inequalities. The results yield explicit rates of convergence in Wasserstein-type distances for several instances of generalized central limit theorems.