2020/04/16 by Neelesh S. Upadhye, Kalyan Barman, Upadhye, Neelesh S +1
Decision Sciences · Mathematics · #60E07 #60E10 #60F05 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2004.07593
openalex publication_date 2020/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we first review the connection between Lévy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the Lévy-Khinchine representation of the characteristic function, we establish a Stein identity for an infinitely divisible random variable. The classification and slight modification in approach give us a Stein identity for an α-stable random variable with α∈ (0,2). Using fine regularity estimates for the solution to Stein equation, we derive error bounds for α-stable approximations. We then apply these results to obtain rates of convergence. Finally, we compare these rates with the results available in the literature.