N. A. Elizarova, A. E. Condratenko, N. A. Kondratenko, V. N. Sobolev, D. A. Chernyshova, “On the convergence of the fractional part of convolutions of Poisson distributed random variables with unequal parameters”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2025, Issue 3,Pages <nobr>45

Theory of Probability and Mathematical Statistics

On the convergence of the fractional part of convolutions of Poisson distributed random variables with unequal parameters

N. A. Elizarova^a, A. E. Condratenko^b, N. A. Kondratenko^c, V. N. Sobolev^b, D. A. Chernyshova^b

^a MIREA — Russian Technological University, Moscow
^b Lomonosov Moscow State University, Moscow
^c Moscow Institute of Physics and Technology, Moscow

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: convolution, fractional part, uniform distributions, Poisson distribution, entropy.

UDC: 512.64, 517.926, 517.962.26, 517.982.43, 519.21, 519.72

MSC: Primary 60F05; Secondary 60F99.

Received: 16.07.2025
Revised: 20.09.2025
Accepted: 06.10.2025

DOI: 10.26456/vtpmk753