On the central limit theorem in Banach spaces

Aloisio Araujo

Journal of Multivariate Analysis, 1978, vol. 8, issue 4, 598-613

Abstract: It is shown, with the use of a concentration inequality of LeCam, that associated with an infinitely divisible random variable with values in a separable Banach space there is a Lévy-Khintchine formula. A partial converse of this fact is also proved. Relations between the continuity of the compound Poisson and the Gaussian variables associated with a Lévy measure are studied. A central limit theorem is obtained and examples are given.

Keywords: Central; limit; theorem; in; Banach; spaces; LeCam; concentration; inequality; Lévy-Khintchine; representation; in; Banach; spaces (search for similar items in EconPapers)
Date: 1978
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Citations: View citations in EconPapers (4)

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