The Paradigm of Complex Probability and Regular Markov Chains

The crucial job of the theory of classical probability is to compute and 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 foundation 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 with 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.