Using stochastic methods in geosciences has become very popular in recent years. Random function or random field is an essential concept in many models for geoscience applications. In this lecture, firstly, we will focus on the important class of stationary Gaussian random fields and discuss an algorithm for their simulation, based on the spectral representation theory of stationary random fields. Then we are going to introduce two other classes of stationary random fields which we think are important for geoscience applications: Markov random fields and random fields with Poisson-type spectrums. Some ideas for simulation in these cases will be discussed, among which are MCMC algorithms with local evolution rules.

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