Simulation & Optimization: Poisson Process & Random Numbers

This lecture covers the pitfalls of simulation, focusing on the mean and challenges of generating draws from complex systems. It explains the use of pseudo-random numbers and the inverse transform method for discrete distributions. The lecture delves into the acceptance-rejection method for discrete distributions and the analysis of acceptance probabilities. It also explores continuous distributions, including the inverse transform method and the rejection method. The lecture concludes with a discussion on Monte-Carlo integration, variance reduction techniques, and the simulation of non-homogeneous Poisson processes.