# 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.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Autor
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
Zeitschriftentitel
PROBABILITY THEORY AND RELATED FIELDS
Band
96
Ausgabe
2
Seite(n)
137-151
ISSN
PUB-ID

### 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.
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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