In the year 1933, the Russian mathematician Andrey Nikolaevich
Kolmogorov put forward the system of axioms of modern probability theory. By
adding to Kolmogorov’s original five axioms and an additional three axioms,
this established system can be extended to encompass the imaginary set of
numbers. Accordingly, the complex probability set C will be created and which
is the sum of its corresponding real probability belonging to the real set R
and of its corresponding imaginary probability belonging to the imaginary set
M. Thus, all random phenomena do not occur now in the real set R but in the
general complex set C that encompasses both R and M. Hence, we take into
consideration supplementary new imaginary dimensions to the event occurring in
the ‘real’ laboratory to evaluate the complex probabilities. This is consequently
the objective of this novel paradigm. Subsequently, the outcome of the
stochastic experiments that follow any probability distribution in R is now
predicted perfectly and totally in C and the corresponding probability in the
whole set C is always equal to one. Afterward, it follows that luck and chance
in R are substituted by absolute determinism in C. Therefore, we evaluate the
probability of any probabilistic phenomenon in C by subtracting the chaotic
factor from the degree of our knowledge of the random system. My groundbreaking
Complex Probability Paradigm (or CPP) will be applied to the well-known theory
of Markov Chains Transition Matrices in order to express it perfectly and
absolutely in a deterministic way in the universe C = R + M as well as to extend
it to the probabilities’ universes M and C.
Author(s)
Details
Abdo
Abou Jaoudé
Department of Mathematics and Statistics, Faculty of Natural and
Applied Sciences, Notre Dame University-Louaizé, Lebanon.
Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-48006-18-9/CH2
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