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S. Albeverio, Ya. Goncharenko, M. Pratsiovytyi, G. Torbin

Convolutions of distributions of random variables with independent binary digits

Keywords: Convolutions of singular measures, singular probability distributions, absolutely continuous probability distributions, random variables with independent binary digits

The distribution of a random variable ξ = 2^?kτ_k, where τ_k are independent random variables taking values 0, 1, 2 with probabilities p_ik, i = 0, 1, 2, is investigated.

The behavior of the characteristic function of the r.v. ξ at infinity is studied in details, and necessary and sufficient conditions for singularity resp. absolute continuity of the distribution of the r.v. ξ are found.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 15, 04/2007
Pages: 89 - 104

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