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

What is it about?

The five fundamental axioms of classical probability theory were put forward in 1933 by Andrey Nikolaevich Kolmogorov. Encompassing new imaginary dimensions with the experiment real dimensions will make the work in the complex probability set totally predictable and with a probability permanently equal to one. This is the original idea in my complex probability paradigm. Therefore, this will make the event in C = R + M absolutely deterministic by adding to the real set of probabilities R the contributions of the imaginary set of probabilities M. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Consequently, by calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the real and imaginary and complex probabilities in the probability sets R and M and C and which are all subject to chaos and random effects. Hence, we will apply this novel paradigm to the Law of Large Numbers in order to demonstrate it in an innovative manner and to prove as well in an original fashion an important property at the foundation of statistical physics, additionally it will be applied to the well-known Central Limit Theorem and to demonstrate thus its convergence in a novel way.

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Why is it important?

Computing probabilities is all our work in the classical theory of probability. Adding new dimensions to our stochastic experiment is the innovative idea in the current paradigm which will make the study absolutely deterministic. As a matter of fact, the theory of probability is a nondeterministic theory by essence that means that all the random events outcome is due to luck and chance. Hence, we make the study deterministic by adding new imaginary dimensions to the phenomenon occurring in the “real” laboratory which is R, and therefore, a stochastic experiment will have a certain outcome in the complex probabilities set C. It is of great significance that random systems become completely predictable since we will be perfectly knowledgeable to predict the outcome of all stochastic and chaotic phenomena that occur in nature like for example in all stochastic processes, in statistical mechanics, or in the well-established field of quantum mechanics. Consequently, the work that should be done is to add the contributions of M which is the set of imaginary probabilities to the set of real probabilities R that will make the random phenomenon in C = R + M completely deterministic. Since this paradigm is found to be fruitful, then a new theory in prognostic and stochastic sciences is established and this is to understand deterministically those events that used to be stochastic events in R. This is what I coined by the term “The Complex Probability Paradigm” that was elaborated and initiated in my 25 previous papers.

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