The Paradigm of Complex Probability and The Central Limit Theorem | Chapter 3 | The Paradigm of Complex Probability, the Law of Large Numbers, and the Central Limit Theorem

The concept of mathematical probability was established in 1933 by Andrey Nikolaevich Kolmogorov by defining a system of five axioms. This system can be enhanced to encompass the imaginary numbers set after the addition of three novel axioms. As a result, any random experiment can be executed in the complex probabilities set C which is the sum of the real probabilities set R and the imaginary probabilities set M. We aim here to incorporate supplementary imaginary dimensions to the random experiment occurring in the “real” laboratory in R and therefore to compute all the probabilities in the sets R, M, and C. Accordingly, the probability in the whole set C = R + M is constantly equivalent to one independently of the distribution of the input random variable in R, and subsequently the output of the stochastic experiment in R can be determined absolutely in C. This is the consequence of the fact that the probability in C is computed after the subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic experiment. We will apply this innovative paradigm to the well-known Central Limit Theorem and to prove as well its convergence in a novel way.

Author(s) Details:

Abdo Abou Jaoudé,
Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaize, Lebanon.

Please see the link here: https://stm.bookpi.org/TPCPLLNCLT/article/view/13494