11. ON THE CONVERGENCE OF THE FRACTIONAL PART OF CONVOLUTIONS OF POISSON DISTRIBUTED
RANDOM VARIABLES WITH UNEQUAL PARAMETERS
RANDOM VARIABLES WITH UNEQUAL PARAMETERS
Condratenko, Alexander E., et al. "On the Convergence of the Fractional Part of Convolutions of Poisson
Distributed Random Variables with Unequal Parameters." Global and Stochastic Analysis, vol. 12, no. 5, 2025,
pp. 84–93.
pp. 84–93.
Abstract
The article provides an explicit formula for the distribution of remainders modulo an arbitrary natural number of the
convolutions of unequly distributed Poisson random variables and shows their convergence in law to the uniform
distribution.
Keywords
Key words and phrases. convolution, fractional part, uniform distributions, Poisson distribution, entropy.