ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES
Bentkus V, Götze F (1993)
PROBABILITY THEORY AND RELATED FIELDS 96(2): 137-151.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Bentkus, V;
Götze, FriedrichUniBi
Einrichtung
Abstract / Bemerkung
In Banach spaces the rate of convergence in the Central Limit Theorem is of order O(n-1/2) for sets which have 'regular' boundaries with respect to the given covariance structure and which are three times differentiable. We show that in infinite dimensional spaces it is impossible to weaken this differentiability condition in general, whereas in finite dimensional spaces the assumption of convexity suffices. Similar results hold for the expectation of smooth functionals.
Erscheinungsjahr
1993
Zeitschriftentitel
PROBABILITY THEORY AND RELATED FIELDS
Band
96
Ausgabe
2
Seite(n)
137-151
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/1645467
Zitieren
Bentkus V, Götze F. ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES. PROBABILITY THEORY AND RELATED FIELDS. 1993;96(2):137-151.
Bentkus, V., & Götze, F. (1993). ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES. PROBABILITY THEORY AND RELATED FIELDS, 96(2), 137-151. https://doi.org/10.1007/BF01192130
Bentkus, V, and Götze, Friedrich. 1993. “ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES”. PROBABILITY THEORY AND RELATED FIELDS 96 (2): 137-151.
Bentkus, V., and Götze, F. (1993). ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES. PROBABILITY THEORY AND RELATED FIELDS 96, 137-151.
Bentkus, V., & Götze, F., 1993. ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES. PROBABILITY THEORY AND RELATED FIELDS, 96(2), p 137-151.
V. Bentkus and F. Götze, “ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES”, PROBABILITY THEORY AND RELATED FIELDS, vol. 96, 1993, pp. 137-151.
Bentkus, V., Götze, F.: ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES. PROBABILITY THEORY AND RELATED FIELDS. 96, 137-151 (1993).
Bentkus, V, and Götze, Friedrich. “ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES”. PROBABILITY THEORY AND RELATED FIELDS 96.2 (1993): 137-151.
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