The Paradigm of Complex Probability and Regular Markov Chains

What is it about?

The crucial job of the theory of classical probability is to compute and to assess probabilities. A deterministic expression of probability theory will be achieved by the addition of new dimensions to the stochastic experiments. This is the original and novel idea at the foundations of my paradigm. As a matter of fact, since the events outcomes are due to randomness and chance, then the theory of probability is a nondeterministic system in its essence. A deterministic experiment and hence a stochastic event will have a certain result in the complex probability set C after encompassing novel imaginary dimensions to the chaotic experiment occurring in the real set R. Thus, we will be fully knowledgeable to predict the outcome of stochastic experiments that arise in the real world in all stochastic processes if the random event becomes completely predictable. Hence, extending the real probabilities set R to the deterministic complex probabilities set C = R + M by including the contributions of the set M which is the imaginary set of probabilities, is the work that has been accomplished here. Therefore, a novel paradigm of stochastic sciences and prognostic was laid down in which all stochastic phenomena in R were expressed deterministically in C since this extension was found to be successful. I coined this original model by the term: “The Complex Probability Paradigm” or CPP for short. Knowing that it was illustrated and initiated in my previous research publications. Henceforth, this original probability paradigm will be applied in this work to Regular Markov Chains and Processes.

Featured Image

Why is it important?

Calculating probabilities is the main task of the theory of classical probability. In fact, if we add new dimensions to a random phenomenon it will result to a deterministic expression of the theory of probability. This is the original and novel idea at the foundations of “The Complex Probability Paradigm (or CPP for short)”. As a matter of fact, probability theory is a nondeterministic theory in its core; that means that the outcomes of events are due to chance and randomness. If we add imaginary and new dimensions to a random experiment occurring in the set R it will result to a deterministic experiment and thus a nondeterministic phenomenon will have a certain outcome in the complex probability set C. If the random event becomes completely predictable then we will have perfect knowledge to predict the outcome of random experiments that arise in the real world in all random processes. Consequently, the work that has been accomplished in CPP was to extend the set R of real probabilities to the set C = R + M of deterministic complex probabilities by incorporating the contributions of the set M which is the imaginary probabilities set. Therefore, because this extension was found to be fruitful, then a novel paradigm of prognostic and nondeterministic sciences was established in which all random phenomena in R was defined deterministically. I called this original model "the Complex Probability Paradigm" that was initiated and illustrated in my numerous earlier research publications.

Perspectives