The Shift, properties and recommendations for practical use

Nicolas Bouleau (1)

1 LAMM - Laboratoire de Mathématiques et Modélisation

Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is as wide as that of Monte Carlo method, is particularly relevant when the simulations use, for each sample, a large number of calls to the random function. We give here the theoretical features, the implementation and the specific advantages of this method.

Mots clés: shift; Monte Carlo; simulation; iterated logarithm; ergodic theorem; random number; pointer

Domaines: Probabilités [math.PR]

Nicolas Bouleau. The Shift, properties and recommendations for practical use. 1995, pp.1253. ⟨hal-00109244⟩