Summation arithmetic functions with bounded terms, having a limit normal distribution law

TL;DR

This paper investigates the conditions under which summation arithmetic functions with bounded terms exhibit a normal distribution law, extending understanding of their probabilistic properties and verifying these conditions for known functions.

Contribution

It establishes sufficient conditions for bounded-term arithmetic functions to follow a normal distribution law, with verification for known functions.

Findings

Proves properties of pseudo stationarity and pseudo strong mixing for arithmetic functions.

Identifies sufficient conditions for normal distribution law in summation arithmetic functions.

Verifies conditions for known arithmetic functions.

Abstract

The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Assertions on this topic have been proven. The implementation of these properties for known arithmetic functions has been verified. The article proves a statement about sufficient conditions under which a summation arithmetic function with bounded terms has a limit normal distribution law. The fulfillment of the specified sufficient conditions for known arithmetic functions is considered.