ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: not given Prokhorov, Yuri, Steklov Mathematical Institute, Moscow, Russia A characterisation problem for quadratic forms in random variables Let Q(x_{1}, …, x_{n}) be a positive definite quadratic form, X_{1}, …, X_{n} i. i. d. random variables, Z_{1}, …, Z_{n} i. i. d. standard normal variables. If Q(X_{1}, …, X_{n}) =^{d} Q(Z_{1}, …, Z_{n}) and the distribution of X-es is symmetric then X_{j} =^{d} Z_{j} (U =^{d} V means that random variables U and V have the same distribution). This theorem admits many generalizations (they were obtained by V. Ulyanov, G. Kristoff and the author).