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Zeitschrift für Analysis und ihre Anwendungen


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Volume 4, Issue 3, 1985, pp. 257–267
DOI: 10.4171/ZAA/151

Published online: 1985-06-30

Laplace-Gauss Integrals, Gaussian Measure Asymptotic Behaviour and Probabilities of Moderate Deviations

Wolf-Dieter Richter[1]

(1) Universität Rostock, Germany

There is given a general Gaussian measure representation on arbitrary finite dimensional Borel sets. This representation reflects B. Cavalieri’s and E. Torricelli’s "indivisible method" in a modern language. Based upon it, assertions are derived about the Gaussian measure asymptotic behaviour on Borel sets whose distance from the origin tends to infinity. Also two specific multivariate moderate deviation limit theorems for sums of i.i.d. random vectors are deduced.

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Richter Wolf-Dieter: Laplace-Gauss Integrals, Gaussian Measure Asymptotic Behaviour and Probabilities of Moderate Deviations. Z. Anal. Anwend. 4 (1985), 257-267. doi: 10.4171/ZAA/151