I've just had a look at Feller. If you're considering equation (3.1) and Theorem XIII.3.1 thereafter, the problem you're experiencing is typical with Feller... Even though Feller is a great reference (I own both volumes myself), it is not really easy to use, partly because it dates back to the sixties and introduces lots of notation no one else uses (any more?), partly because you constantly have to look several pages back in order to find the currently active hypotheses. In this case, remember that the "attribute"

is what he calls a "recurrent event", and if you look up the definition, you can see that "

" is not a recurrent event because condition (b) fails (I should say: you can see that the attribute

such that the finite sequence of states

has the attibute

iff

, is not a recurrent event...). It is a recurrent event only under the probability

, not under

.