ABSTRACT
This chapter deals with Markov processes having parameter setT = [0,oo) and state space Z = {0, ±1, ±2,...} or subsets of it.
e Z, the following relationship holds:
are the transition probabilities o f the Markov chain. A Markov chain is said to be homogeneous if for all i . i e T and i j e Z the transition probabilities Pjj(s,t) de pend only on the difference t-s:
In this case the transition probabilities depend only on one variable. Hence they are written in the form
Note: This chapter considers only homogeneous Markov chains. Hence no confusion can arise if only Markov chains is referred to. Exceptions are made only when the property of homogeneity is of particular importance.
