ABSTRACT
Here the stochastic kernel P ( z , d y ) defines the support Liarkov chain z,, n 2 0. which is uniformly ergodic in every class X l , 1 5 T 5 L\-i,, 1 5 k 5 i2', and PI (2, dy) and &(z. dy) are perturbing kernels. The former concerns transitions between classes X i and the latter between classes XI;. Of course. these kernels are not stochastic. in particular P l ( x . X ) = P2(z ,X) = 0. for every z E X . The supporting Markov process x ( t ) , t 2 0, is uniformly ergodic too with generator Q.
