ABSTRACT
Deterministic models and stochastic models are two broad categories of mathematical models that aim at providing quantitative characterizations of a real system or a natural phenomenon under study. The salient difference between the two types of models is that, given a set of assumptions for each model, a deterministic model predicts a single outcome, whereas a stochastic model predicts a set of possible outcomes along with the likelihood or probability of each outcome. When a stochastic model is a more suitable choice for the purpose of investigation, it is often the case that the underlying system can be better represented by a collection or a family of random variables, indexed by a parameter such as time or space. Such a family of random variables is called a stochastic process. The field of stochastic processes represents a collection of models and methods used to depict the dynamic relationship of a family of random variables evolving in time or space.
