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Heyde theorem

From Wikipedia, the free encyclopedia

In the mathematical theory of probability, the Heyde theorem is the characterization theorem concerning the normal distribution (the Gaussian distribution) by the symmetry of one linear form given another. This theorem was proved by C. C. Heyde.

Formulation

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Let   be independent random variables. Let   be nonzero constants such that for all . If the conditional distribution of the linear form given is symmetric then all random variables have normal distributions (Gaussian distributions).

References

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