4. Monte Carlo simulation

4.1 Principle

Called Monte-Carlo by von Neumann in allusion to games of chance, the principle of Monte-Carlo simulation is quite simple: it involves replacing analytical calculation with statistical calculation by carrying out a large number of histories of the system under study. It's not unlike walnut shelling (figure 3 ): by simulating random numbers, we shake the system in all directions and, just as the ripest walnuts fall first, the events with the highest probability appear first.

The outside joke should not obscure the depth of the preceding analogy: Monte-Carlo simulation is self-approximating. Unlike the analytical approach, where lengthy mathematical demonstrations...