Summary
LetX, X 1 ,X 2 ,... ∈B denote a sequence of i.i.d. random variables of a real separable Banach spaceB, Y ∈ B denote a Gaussian random variable. Suppose thatEX=EY=0 and that covariances ofX andY coincide. DenoteS n =n −1/2 (X 1 +...+X n ). We prove that under appropriate conditions
and give estimates of the remainder term. Applications to theω 2, the Anderson-Darling test and to the empirical characteristic functions are given.
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Bentkus, V., Račkauskas, A. On probabilities of large deviations in Banach spaces. Probab. Th. Rel. Fields 86, 131–154 (1990). https://doi.org/10.1007/BF01474639
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DOI: https://doi.org/10.1007/BF01474639
Keywords
- Covariance
- Banach Space
- Stochastic Process
- Characteristic Function
- Probability Theory