A graduate-level treatment of generating pseudo-random samples and using them to estimate quantities that resist deterministic computation. Covers random-variate generation by inverse-transform and acceptance-rejection sampling; Monte Carlo integration and its dimension-independent O(1/sqrt(N)) error justified by the law of large numbers and central limit theorem; variance reduction via importance sampling; simulation of stochastic processes (Markov chains, random walks, Poisson and Gaussian processes); the stochastic simulation algorithm (Gillespie/SSA) for Markov jump processes; and Markov-chain Monte Carlo via the Metropolis-Hastings algorithm for sampling from complex target distributions.
Lecture notes (Davoud Mirzaei, Uppsala University) giving a graduate-level introduction to stochastic simulation and the Monte Carlo method. Contrasts deterministic and stochastic computation, then d…