Application to the Examples of Part I

The aim of this chapter is to provide criteria under which Assumption (A.4) of the previous chapter is valid. We shall see that the algorithms given in Part I satisfy the general assumptions of Chapter 1; thus the conclusions of the theorems involving approximation by solution of the ODE (Theorems 9 and 14) and of the theorems involving asymptotic approximation (Theorems 13, 14, 17) may be applied to these algorithms. As previously noted in Chapter 1, Subsection 1.1.3, comment c, in verifying that Assumption (A.4) is satisfied, we shall require that the Markov chain with transition probability Π _θ is ergodic, and the functions Π _θ H _θ are regular in θ.