Markov Chains and Ergodic Theorems
Onésimo Herná-Lerma, Jean Bernard Lasserre · Birkhäuser Basel eBooks · 2003
In this chapter we first state the definition of a Markov chain (MC) with values in a general measurable space (X. B) , and then present some basic ergodic theorems for functionals of MCs. In fact, in §2.2 we introduce several equivalent ways of defining a MC. This is important to keep in mind because in some concrete situations, one of these definitions or formulations might be more appropriate than the others. For instance, in engineering and economics, many of the MC models are expressed by a “state equation” (as in (2.2.4), below). but there are cases — e.g., in epidemics and fisheries modelling --- in which it might be more practical to describe a MC using “transition probabilities” (as in (2.2.2)) rather than a state equation.