Bounds for the accuracy of Poissonian approximations of stable laws

Bentkus V, Götze F, Paulauskas V (1996)
STOCHASTIC PROCESSES AND THEIR APPLICATIONS 65(1): 55-68.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Stable laws G(alpha) admit a well-known series representation of the type [GRAPHICS] where Gamma(1), Gamma(2), ... are the successive times of jumps of a standard Poisson process, and X(1), X(2), ..., 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 S-n = Sigma(j=1)(n) Gamma(j)(-1/alpha)X(j), and we get (asymptotically) optimal bounds for the variation of G(alpha)-L(S-n). 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 S-n are also proved.
Erscheinungsjahr
Zeitschriftentitel
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Band
65
Ausgabe
1
Seite(n)
55-68
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Bentkus V, Götze F, Paulauskas V. Bounds for the accuracy of Poissonian approximations of stable laws. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 1996;65(1):55-68.
Bentkus, V., Götze, F., & Paulauskas, V. (1996). Bounds for the accuracy of Poissonian approximations of stable laws. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 65(1), 55-68.
Bentkus, V., Götze, F., and Paulauskas, V. (1996). Bounds for the accuracy of Poissonian approximations of stable laws. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 65, 55-68.
Bentkus, V., Götze, F., & Paulauskas, V., 1996. Bounds for the accuracy of Poissonian approximations of stable laws. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 65(1), p 55-68.
V. Bentkus, F. Götze, and V. Paulauskas, “Bounds for the accuracy of Poissonian approximations of stable laws”, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 65, 1996, pp. 55-68.
Bentkus, V., Götze, F., Paulauskas, V.: Bounds for the accuracy of Poissonian approximations of stable laws. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 65, 55-68 (1996).
Bentkus, V, Götze, Friedrich, and Paulauskas, V. “Bounds for the accuracy of Poissonian approximations of stable laws”. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 65.1 (1996): 55-68.