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Gaussian distribution on a locally compact Abelian group is a generalization of the classical
normal distribution. Roughly speaking, it extends the concept of a normal distribution from the Euclidean space to more general topological groups, i.e., when the group is , it coincides with the usual multivariate normal distribution.
It was introduced by Kalyanapuram Rangachari Parthasarathy, Ranga Rao, and Srinivasa R. S. Varadhan in 1963, see also .
This distribution plays an important role in the representation of characteristic functions of infinitely divisible distributions, the arithmetic of probability distributions, and in characterization problems of mathematical statistics on locally compact Abelian groups.
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