Stochastic models

The mechanism for randomness discussed in this section is the basis for so-called stochastic models now widely used in traditional science. Typically the idea of these models is to approximate those elements of a system about which one does not know much by random variables. (See also page 588.) In the early work along these lines done by James Clerk Maxwell and others in the 1880s, analytical formulas were usually worked out for the probabilities of different outcomes. But when electronic computers became available in the 1940s, the so-called Monte Carlo method became increasingly popular, in which instead explicit simulations are performed with different choices of random variables, and then statistical averages are found. Early uses of the Monte Carlo method were mostly in physics, particularly for studies of neutron diffusion and particle shower generation in high-energy collisions. But by the 1980s the Monte Carlo method had also become common in other fields, and was routinely used in studying for example message flows in communication networks and pricing processes in financial markets. (See also page 1192.)