The set of imaginary numbers is taken into account by
extending the probability system of five axioms of Andrey Nikolaevich
Kolmogorov which was put forward in 1933. This is achieved by adding three new
and supplementary axioms. Hence, any random experiment can thus be performed in
the extended complex probability set C = R + M which is the sum of the real set
R of real probabilities and the imaginary set M of imaginary probabilities. The
objective here is to determine the complex probabilities by encompassing and
considering additional new imaginary dimensions to the event that occurs in the
“real” laboratory. The outcome of the stochastic phenomenon in C can be
foretold perfectly whatever the probability distribution of the input random
variable in R is since the corresponding probability in the whole set C is
permanently and constantly equal to one. Thus, the consequence that follows
indicates that randomness and chance in R is substituted now by absolute
determinism in C. This is the result 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. This novel complex probability
paradigm will be applied to numerical analysis and to chaos theory to prove
henceforth that chaos vanishes totally and completely in the probability
universe C = R + M.
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/TPCPNACT/article/view/14275
No comments:
Post a Comment