Markov chains: notions, properties and simulation algorithms
Radu Stefan Stoica · 2025
To simulate marked point processes, it is often necessary to use Markov Chain Monte Carlo (MCMC) techniques. The Metropolis-Hastings algorithms are MCMC techniques that can be considered relatively easy to implement. This chapter discusses Metropolis-Hastings and perfect simulation algorithms. First, Markov chains on general state spaces 90 and their properties are introduced. These concepts are then used to construct a Metropolis-Hastings algorithm for marked point processes, with a focus on its convergence properties. Finally, it introduces the principle of the Coupling From the Past perfect sampler, its theoretical properties and its implementation for the simulation of locally stable marked point processes.