Stochastic modelling: art and science

The purpose of this paper is to outline an approach to stochastic modelling, based on explicit hypotheses formulation and the application of elementary probability rules to determine corresponding stochastic processes. Applications including the Poisson process, the random walk hypothesis for stock market prices and other problems are outlined and referred to. Emphasis is given to model construction and not to its analysis. Through the examples treated several approaches to stochastic modelling analysis are highlighted, which are mostly used in stochastic modelling courses in industrial, business and engineering schools. Throughout the paper, it is stressed that, although stochastic modelling and analysis is a science, it is also an art, for it requires that we distinguish the known from the unknown and construct models that account for behaviours and evolutions which we might not, a priori, be aware of.