A. E. Kondratenko, V. N. Sobolev, “Generalization and unification of the concepts of remainder of division and fractional part, maximization of entropy of fractional part of convolution with uniform distribution”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2022, Issue 1,Pages <nobr>45

Theory of Probability and Mathematical Statistics

Generalization and unification of the concepts of remainder of division and fractional part, maximization of entropy of fractional part of convolution with uniform distribution

A. E. Kondratenko^a, V. N. Sobolev^b

^a Lomonosov Moscow State University, Moscow
^b Laboratory of TVP, Moscow

Abstract: The article considers the issue of preserving the information property of convolution with canonical uniform distribution in the cases of arbitrary finite lattice and arbitrary segment. For this purpose, the generalization and the unification of the concepts of remainder of division and fractional part are proposed.

Keywords: convolution, fractional part, uniform distribution, entropy.

UDC: 517.962.26, 517.982.43, 519.21, 519.72

Received: 14.02.2022
Revised: 16.03.2022

DOI: 10.26456/vtpmk628