Calculating probabilities is a crucial task of classical
probability theory. Adding supplementary dimensions to nondeterministic
experiments will yield a deterministic expression of the theory of probability.
This is the novel and original idea at the foundation of my complex probability
paradigm. As a matter of fact, probability theory is a stochastic system of
axioms in its essence; that means that the phenomena outputs are due to
randomness and chance. By adding novel imaginary dimensions to the non-deterministic
phenomenon happening in the set R will lead to a deterministic phenomenon and
thus a stochastic experiment will have a certain output in the complex
probability set C. If the chaotic experiment becomes completely predictable
then we will be fully capable of predicting the output of random events that
occur in the real world in all stochastic processes. Accordingly, the task that
has been achieved here was to extend the random real probabilities set R to the
deterministic complex probabilities set C = R + M and this by incorporating the
contributions of the set M which is the associated and complementary imaginary
set of probabilities to the set R. Hence, the probability in C is computed
after the subtraction of the chaotic factor from the degree of our knowledge of
the nondeterministic experiment. Consequently, since this extension was
revealed to be successful, then an innovative paradigm of stochastic sciences
and prognostic was put forward in which all nondeterministic phenomena in R
were expressed deterministically in C. I coined this novel model with the term
"The Complex Probability Paradigm (or CPP)" which was initiated and
established in my earlier research works. Moreover, this pioneering paradigm
will be applied in a creative manner to the stochastic procedures and
algorithms of the famous and historical Buffon’s needle method to compute PI,
to the renowned neutron shielding problem, and to numerous and various topics
that arise in Monté Carlo Methods.
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/978-93-48006-59-2
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