Numerical Methods for Stochastic Processes

Stochastic models deal with mathematical expectations (the probability of events, variance, etc). This study deals with the calculation of these mathematical expectations, primarily by simulation methods. It explores the numerical use of the shift method, which has considerable advantages as far as computers are concerned. The authors present the main methods and ideas in the field, and signal the sort of problems raised by new methods. Topics presented include Monte Carlo and quasi-Monte Carlo methods, the simulation of major stochastic processes and deterministic methods adapted to Markovian problems, as well as special problems related to stochastic integral and differential equations.