The simulation methods are needed and applied as tools to analyse, in a possibly simpler way, some complex stochastic phenomena modelled in physics, biology or in engineering. The fast developments of probability theory and computer science have presented us with more realistic and sophisticated stochastic processes to model complex random phenomena arising in physics, biology and other branches of engineering sciences. These stochastic models are often based on the simulation of high dimensional stochastic processes, including nonlinear stochastic partial differential equations. The source of randomness often comes from unknown initial conditions, and from the uncertainties of the models, including unknown kinetic parameters. The sophisticated stochastic search models belong to the class of Markov chain Monte Carlo methods (MCMC), and particle simulation techniques also called sequential Monte Carlo methodologies (SMC). In computational physics, as well as in stochastic optimization, we are interested in computing Boltzmann-Gibbs distributions associated with an inverse temperature parameter ß.