Stochastic Simulation

CHAPTER 1

Aims of Simulation

The terminology of our subject can be confusing, with some authors insisting on shades of meaning that do not have widespread agreement. A dictionary definition of “to simulate” is

Feign, . . . , pretend to be, act like, resemble, wear the guise of, mimic, . . . imitate conditions of (situation etc.) with model, for convenience or training. . . .

Concise Oxford Dictionary, 1976 ed.

In everyday usage “simulated” has a derogatory ring, but the value of simulators in training pilots is also recognized. In its technical sense simulation involves using a model to produce results. rather than experiment with the real system under study (which may not yet exist). For example, simulation is used to the explore the extraction of oil from an oil reserve. If the model has a stochastic element, we have stochastic simulation, the subject of this monograph.

Another term, the Monte-Carlo method, arose during World War II for stochastic simulations of models of atomic collisions (branching processes). Sometimes it is used synonymously with stochastic simulation, but sometimes it carries a more specialized meaning of “doing something clever and stochastic with simulation.” This may involve simulating a different system from that under study, perhaps even using a stochastic model for a deterministic system (as in Monte-Carlo integration). We will not use Monte Carlo except in the conventional terms “Monte-Carlo integration” and “Monte-Carlo test.”

Simulation can have ...