Using Vector Representations of Characteristic Functions and Vector Logarithms When Proving Asymptotic Statements
Abstract
In this methodological–technical note, in addition to the well-known concepts of logarithms of positive real numbers and operators, we open a path for mathematical treatment of the mathematical concept of the logarithm of a vector. We prove the most basic arithmetic operations for this new logarithm concept and demonstrate how it applies to characteristic functions and limit theorems of probability theory. As a side result, we revise a formula for ii that is known from the literature.
Fields of Study & Subjects
Probability and Statistical Research
Mathematical and Theoretical Analysis
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Stats
- Volume
- 9
- Issue
- 1
- Pages
- 16–16
- Publication date
- 11 February 2026
- Language
- EN