Bounds for the accuracy of Poissonian approximations of stable laws

V. Bentkus, F. Götze and V. Paulauskas

Stochastic Processes and their Applications, 1996, vol. 65, issue 1, 55-68

Abstract: Stable law Gz admit a well-known series representation of the type where [Gamma]1, [Gamma]2, ... are the successive times of jumps of a standard Poisson process, and X1, X2, ..., denote i.i.d. random variables, independent of [Gamma]1, [Gamma]2, ... We investigate the rate of approximation of G[alpha] by distributions of partial sums Sn = [summation operator]nj = 1 [Gamma]-1/[alpha]jXj, and we get (asymptotically) optimal bounds for the variation of . 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: Stable; laws; Poissonian; representation; Convergence; in; variation; Convergence; rates; Berry-Esseen; bounds; Concentration; functions (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (2)

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