Title of article
Bounds for the accuracy of Poissonian approximations of stable laws
Author/Authors
Bentkus، V. نويسنده , , V. and Gِtze، نويسنده , , F. and Paulauskas، نويسنده , , V.، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 1996
Pages
14
From page
55
To page
68
Abstract
Stable law Gz admit a well-known series representation of the type
Γ1, Γ2, … are the successive times of jumps of a standard Poisson process, and X1, X2, …, denote i.i.d. random variables, independent of Γ1, Γ2, … We investigate the rate of approximation of Gα by distributions of partial sums Sn = ∑nj = 1 Γ−1αjXj, and we get (asymptotically) optimal bounds for the variation of Gα − L(Sn). The results obtained complement and improve the results of A. Janicki and P. Kokoszka, and M. Ledoux and V. Paulauskas. Bounds for the concentration function of Sn are also proved.
Keywords
Poissonian representation , Convergence in variation , Stable laws , Concentration functions , Convergence rates , Berry-Esseen bounds
Journal title
Stochastic Processes and their Applications
Serial Year
1996
Journal title
Stochastic Processes and their Applications
Record number
1575972
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