Introduction to Markov Processes
Nicolas Chopin, Omiros Papaspiliopoulos · Springer series in statistics · 2020
SummaryWe introduce Markov processes using probability kernels. This allows us to define state-space models with wildly different state-spaces and dynamics in a common framework. We study two basic sets of properties of the probability distributions of such processes: the evolution of marginal distributions via recursions, and the structure of conditional distributions. In terms of the latter, we discuss the notion of conditional independence; when the Markov process consists of two components, , we study the distribution of conditional on ; we call the process whose distribution is this conditional distribution a partially observed Markov process. We show that state-space models are instances of this framework.