RATE OF CONVERGENCE TO ALPHA STABLE LAW USING ZOLOTAREV DISTANCE : TECHNICAL REPORT

Solym Manou-Abi (1, 2)

1 CUFR - Centre Universitaire de Formation et de Recherche de Mayotte
2 IMAG - Institut Montpelliérain Alexander Grothendieck

This paper considers the question of the rate of convergence to α-stable laws, using arguments based on the Zolotarev distance to prove bounds. We provide a rate of convergence to α-stable random variable where 1 < α < 2, in the generalized CLT, that is, for the partial sums of independent identically distributed random variables which are not assumed to be square integrable. This work is a technical report based on the Zolotarev paper in [1].

Mots clés: AMS Subject Classification : 60F05; 60G52; 60E07 Key words and phrases: CLT; Probability metric; Rate of convergence; Stable law

Domaines: Mathématiques [math]; Statistiques [stat]

Solym Manou-Abi. RATE OF CONVERGENCE TO ALPHA STABLE LAW USING ZOLOTAREV DISTANCE : TECHNICAL REPORT. [Research Report] CUFR de Mayotte et IMAG Montpellier, France. 2017. ⟨hal-01672804⟩