ABSTRACT
In this chapter, the author provides a detailed theoretical discussion of the embedding techniques, as well as series of illustrative examples that include spatially inhomogeneous models and time inhomogeneous models. It is concerned with the continuous time version of a Markov chain. Embedding techniques allow the author to calculate continuous time versions of Markov chains. Such embeddings allow the author to study properties of a chain via properties of the related infinitesimal generators. The chapter discusses spatial Poisson point processes, effective simulation techniques of these time inhomogeneous models for bounded and continuous intensity functions λt. It emphasizes that the sampling technique is based on the Poisson thinning properties.
