Fundamental Mathematical Methods and Concepts

In the current manuscript, we will apply to the well-known and established theory of Markov Chains my groundbreaking and novel Complex Probability Paradigm (or CPP) which will lead to a completely and perfectly deterministic expression of these stochastic processes in the universe of probabilities C = R + M. Consequently, it is important before “probing the depths” of Markov Chains, that we define in this chapter some essential mathematical concepts and fundamental tools and theorems that will be extensively used in the whole manuscript algorithms and C++ programs.