Abstract
On the hyperbolic spaces of the form G/K a fairly complete theory of spherical functions is available in order to study Fourier transforms of K-biinvariant probability measures on G. The differentiability of this Fourier transform enables us to introduce the notion of variance. Moreover, continuous convolution semigroups of probability measures admit a Lévy-Khintchine representation, and so Gaussian semi-groups can be defined via their Fourier transforms. The aim of our discussion is to establish sufficient conditions in terms of variances for a triangular system of K-biinvariant probability measures on G to converge towards a Gaussian measure.
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© 1981 Springer-Verlag
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Heyer, H. (1981). An application of the method of moments to the central limit theorem on hyperbolic spaces. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097315
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DOI: https://doi.org/10.1007/BFb0097315
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