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Article

On Properties of Polynomials in Random Elements

Theory Probability and its Applications. 2016. Vol. 60. No. 2. P. 325-336.
Translator: V. V. Ulyanov.

This paper deals with different properties of polynomials in random elements: bounds for characteristic functionals of polynomials, a stochastic generalization of the Vinogradov mean value theorem, the characterization problem, and bounds for probabilities to hit the balls. These results cover the cases when the random elements take values in finite as well as infinite dimensional Hilbert spaces.